Trade In Fantasy Ch. 3: Routine Personnel Pt 2
The 2nd of likely four posts looking at everyday personnel in Trade. In this part, Beasts of Burden, Provisions, Carts, and Wagons.
For anyone wondering at the cause of the delay, just look at the number of tables that I’ve ended up using in this post – then remember that each of them has to be hand-coded as well as having the data generated and checked.
Add to that the custom diagrams – six of them, art last count – which can take hours to generate, and it should be clear that I have not been idle!
I thought about splitting the post, but the logical division point comes relatively early; it would not have been a post up to Campaign Mastery’s normal standards. Furthermore, each time I do that, I have to source a new chapter title graphic – sometimes easy to do, sometimes hard and taking more hours.
Sometimes, it just takes longer. All you can do is hope that it was worth the wait!
Credit where it’s due:
The series title graphic combines three images: The Clipper Ship Image is by Brigitte Werner (ArtTower); Dragon #1 is by Parker_West; and Dragon #2 is by JL G. All three images were sourced from Pixabay.
Table Of Contents: In part 1 of Chapter 3: Routine Personnel (last time)
3.1 A Choice Of Four Trade Unit Standards (actually, 8)
3.1.0 Principles of Comparative Modes Of Transport
3.1.1 Humans as a beast of burden
3.1.1.1 Lift from STR
3.1.1.2 Average isn’t Average
3.1.1.3 4d6 keep 3 vs 3d6
3.1.1.4 Career Paths & STR3.1.1.4.1 Linear vs Non-Linear
3.1.1.5 Lift, at last
3.1.1.6 EncumbranceSidebar: Behind The Curtain
3.1.1.7 Load & Load Capacity
3.1.1.8 Load Balance3.1.1.8.1 Adding a Staff to the equation
3.1.1.8.2 Relating Load to Encumbrance (D&D)
3.1.1.8.3 Relating Load to Encumbrance (Hero / Superhero)
3.1.1.8.4 Relating Load to Encumbrance (Hero / Adventurer’s Club)3.1.1.9 Load Distribution
3.1.1.10 Humanoids3.1.1.10.1 The Size Factor
3.1.1.10.2 The Proportions Factor
3.1.1.10.3 The Racial Factor
3.1.1.10.4 The Human Advantage
3.1.1.10.5 The Iconic Reference
3.1.1.10.6 Elves
3.1.1.10.7 Dwarves
3.1.1.10.8 Halflings
3.1.1.10.9 Orcs
3.1.1.10.10 Ogres
3.1.1.10.11 Bugbears
3.1.1.10.12 Trolls
3.1.1.10.13 Hill Giants
3.1.1.10.14 Stone Giants
3.1.1.10.15 Other Giants
3.1.1.10.16 OthersIn This post:
3.1.1 Humans as a beast of burden (cont)
3.1.1.11 Time: 8, 12, 16, 24
3.1.1.12 Speed
3.1.1.12.1 Non-D&D Scales3.1.1.13 Provisions: Food
3.1.1.14 Provisions; Water
3.1.1.15 Replenishment: Foraging / Hunting / Buying
3.1.1.16 Distance
3.1.1.17 The humanoid bottom line3.1.1.17.1 Elves
3.1.1.17.2 Dwarves
3.1.1.17.3 Halflings
3.1.1.17.4 Orcs
3.1.1.17.5 Ogres
3.1.1.17.6 Bugbears
3.1.1.17.7 Trolls
3.1.1.17.8 Hill Giants
3.1.1.17.9 Stone Giants
3.1.1.17.10 Other Giants
3.1.1.17.11 Other Humanoids3.1.2 Horses as a beast of burden
3.1.3 Burros as a beast of burden
3.1.4 Carts as a ‘beast of burden’
3.1.4.1 Strength of the Axles
3.1.4.1.1 Cart & Wagon Stats: High-Score Option
3.1.4.1.2 Cart & Wagon Stats: Low-Score Option
3.1.4.1.3 Cart & Wagon Axle Reinforcement3.1.4.2 Strength of the Wheels
3.1.4.2.1 Spoke Thickness
3.1.4.2.2 Number Of Spokes
3.1.4.2.3 Solid Wheels3.1.4.3 Strength of the Connection
3.1.4.4 Strength of the Bed
3.1.4.5 Rolling Resistance
3.1.4.5.1 Slope (aka Grade, Gradient, Stepth, Incline, Mainfall, Pitch, and Rise)3.1.4.6 Gravity Vector
And, Further down the track (1-2 more posts):
3.1.5 Choosing Your Unit
3.1.6 Ramifications
3.1.6.1 Freight Management
3.1.6.2 Base Loading Time
3.1.6.3 On The Road: Drivers, Guards, Cargo-masters, & Handlers
3.1.6.4 Base Unloading Time
3.1.6.5 Sales Prep
3.1.6.6 Sales and Customers3.2 Recruiter / Personnel Manager
3.2.1 Assumption #1: The best available gets hired
3.2.1.1 Any Relevant Skill
3.2.1.2 INT + WIS
3.2.1.3 Substituting CHAR3.2.2 Assumption #2: They Hire The Best
3.2.3 The Principle Of Labor Unmanagement3.3 The Labor Unit
3.3.1 Eight man-hour Labor Units
3.3.2 Twelve man-hour Labor Units
3.3.3 Sixteen man-hour Labor Units
3.3.4 Twenty-four man-hour Labor Units
3.3.5 Choices and Expectations3.4 The Labor Market
3.5 Basic Pay-scales
3.5.1 Pick An Index
Which will be followed by:
3.6 Productivity
3.6.1 Premium Labor Units
3.6.2 Reminder: Profit per Trade Unit, not costs or prices3.7 Pay-scale Variations
3.7.1 Overpaying workers / Elite Quality Workforce
3.7.2 Underpaying workers / Lower Quality Workforce
3.7.3 Slaves
3.7.4 Minor Stakeholders
3.7.5 Combinations & Complications3.8 Technological Impact
3.8.1 Major Breakthroughs
3.8.2 Incremental Gains
3.8.3 Trade Secrets & Industrial Spies3.9 Key Personnel & The Labor Unit
3.10 The Personnel Bottom LineIn future parts after that:
- Mode Of Transport
- Land Transport
- Waterborne Transport
- Spoilage
- Key Personnel
- The Journey
- Arrival
- Journey’s End
- Adventures En Route
Recap:
In the last post, I showed how to determine an answer to the question “How much can one carry”, not only for humans but for all humanoids.
The solution offered takes into account every variable that could be thought of, from STR to Stamina to size and proportions (when it comes to non-humans).
It also presented a couple of key equations that will really come into relevance in today’s post:
Work Effort = Bulk × Distance / Labor Unit Standard.
where,
Bulk is as defined in Chapter Two: Volume × Weight, measured in Cargo Units;
Distance is how far the chosen Trade Unit Standard Transport can move a Cargo Unit in a certain period of time; and
“Labor Unit Standard” defines that period of time.In other words,
Work Effort = Bulk × Speed.
It was then determined that the average STR for a human who uses STR for a living should be 11 (D&D/Pathfinder scale) or 10 (Hero System scale). This was based on Lift values of 225.54 lb and 102.28 kg, respectively.
There was also discussion of the fact that the normal STR maximums in both systems gave Lift values roughly triple the actual current world records). Nothing was done about that in terms of corrections to stat progression – it was left to individual GMs to determine what to do about the fact.
Carrying capacity is used differently depending on how the load is balanced and distributed, but the bottom line is that any given humanoid has a capacity which determines how much the loads that can be considered “cargo” can weigh.
Load is the effective weight being carried by the character.
Load Capacity is the character’s capacity to carry a Load.
Loads can be Distributed, Supported, or Point.. Distributed loads are worn, supported loads are carried on the back and/or shoulders, and point loads are just carried.
Unused Capacity is the Character’s adjusted Load Capacity (size, shape, racial adjustments) minus adjusted Distributed and Supported Load totals.
Therefore, Unused Capacity can be used to carry Cargo. The weight that produces this amount of Load (maximum) can be determined by multiplying the Unused Capacity by various factors (Balance, character size, shape, and race) – in reality, the actual Cargo Weight is being multiplied by the inverse of these factors, but this is is the easiest way to get a maximum.
There were also modifiers for teams of characters carrying a single load, and for the use of walking sticks and staffs.
Once a maximum has been determined, actual Cargo weights can be adjusted to determine the actual Load, and therefore the Encumbrance affecting the character, which limits the characters Speed of Movement (amongst other effects).
Unfortunately, there’s no clear and consistent way of doing so, it varies from one game system to another.
It must be emphasized that while the systems can be employed for individuals, the goal was actually to define a racial “average”.
Finally, something I’ve described as “The Human Advantage” was defined:
- 5 movement rate (“), after adjusting for Load Encumbrance, can be sustained for 2 hours.
- -10 movement rate (“), after adjusting for Load Encumbrance, can be sustained for 4 hours or CON hours, whichever is lower.
- -15 movement rate (“), after adjusting for Load Encumbrance, can be sustained for 8 hours or CON hours, whichever is lower.
- -20 movement rate (“), after adjusting for Load Encumbrance, can be sustained for one hour per point of CON or for 1 day, whichever is lower.
Some races have an even greater serving of this ability, others less, and many don’t have it at all. But those other races, generally, don’t have it in as broadly applicable form as Humans – it might advantage them with loads carried a certain way, or only when balanced, or are otherwise compromised.
Al caught up? Good, then let’s dive right in…
- Poor Grazing: 112.5 g × 0.06218 = 6.99525 = 7 minutes work.
- Average Grazing: 225 g × 0.06218 = 13.9905 = 14 minutes work.
- Good Grazing: 337.5 g × 0.06218 = 20.98575 = 21 minutes work.
- Excellent Grazing: 450 g × 0.06218 = 27.981 = 28 minutes work.
- Poor Grazing: 60 + 7 = 67 minutes so
60 × 60 / 67 of an hour lets the horse work for the rest of the hour = 53.7 minutes.
Call it 54 minutes grazing for 6 minutes work. - Average Grazing: 60 + 14 minutes = 74;
60 / 74 × 60 = 48.65 minutes.
48.65 minutes grazing for 11.35 minutes work. - Good Grazing: 60 + 21 minutes = 81;
60 / 81 × 60 = 44.44 minutes.
44.44 minutes grazing for 15.56 minutes work. - Excellent Grazing: 60 + 28 minutes = 88;
60 / 88 × 60 = 40.91 minutes.
40.91 minutes grazing for 19.09 minutes work.
For reasons that I’ll get into in section 3.3, time in this system is measured in lumps of 8, 12, 16, or 24 hours, depending on circumstances. The time element of a labor unit therefore has to operate with all these intervals. We also want it to be as large as possible to keep the number of Labor Units involved down to a manageable number, and reasonably small to minimize pesky decimal places.
With those requirements, defining the labor unit in terms of 4 man-hours per person is the obvious best choice.
We are closing in on an answer to the question, “How far can the typical human porter carry a load in a single Labor Unit’s worth of time?”
Speed × Time = Distance, that should be obvious. The base human speed – D&D Scale – is 30 feet in a round. How long is a round?
In Combat, it’s 6 seconds – so 10 of them in a minute, 600 of them in an hour, and 2400 of them in four hours.
So the base movement – D&D scale – is 2400 × 30 = 72,000 feet, or 13.64 miles (21.95 km).
The immediate question is, what does this have to do with the price of barley in outer woop-woop?
A long time ago, I did some basic research on movement rates:
★ Normal Walking Pace = 2.5 to 4* mph, usually 3 mph.
★ Fast Walking Pace = 3.5 to 5* mph.
★ March = 100 yards / minute = 3.4 mph
★ Fast March = 160 / 116 × above = 4.7 mph
★ Forced March: 4.16 – 4.785 mph
★ Jog = 4 to 6* mph
★ Distance Running, Male: 80% of Run = 8-9.6 mph
★ Distance Running, Female: 80% of Run = 6.4-8 mph
★ Normal Run, Male: 10-12 mph
★ Normal Run, Female: 8-10 mph
★ Fast Run, Male: 12-15 mph
★ Fast Run, Female: 10-13 mph
Records:
★ Fastest non-professional individual 200km run**: 29 hs 42 min = 6.73 mph
★ Marathon Record Pace = 42.2 km / 2 h = 21.1 km/h = 13.111 mph
★ Fastest 200m run, Male: 19.19 sec = 37.52 kph = 23.3 mph
★ Fastest 200m run, Female: 19.3 sec = 37.3 kph = 23.18 mph
★ Fastest 100m run, Male: 9.58 sec = 37.56 kph = 23.34 mph
★ Fastest 100m run, Female: 10.49 sec = 34.3 kph = 21.31 mph
* Top speed is only possible to humans in very good health & fitness
** Athletes can run 200-270 km in 24 hrs = 8.33 – 11.25 mph
Age Effect:
★ Child <9: × 0.525, Encumbrance × 2
★ Male Adult: × 0.958, Encumbrance × 1
★ Female Adult: x0.967, Encumbrance × 0.905
★ Male Senior Fit: x0.967, Encumbrance × 1.16
★ Female Senior, Fit: x0.817, Encumbrance × 1.10
★ Over 70***: x0.725, Encumbrance × 2.5
*** if possible at all
To that, we need to allow for terrain, but that gets complicated. As rules of thumb:
★ Good Road, Level: x1
★ Bad Road, Level: x0.8
★ Broken Ground, Level: x0.6
(Working Average: x0.75)
★ Undergrowth, thick: As above, x0.8
★ Undergrowth, very thick, As above × 0.5
★ Swamp / Marsh / Mud: As above × 0.3
★ Downhill: As above, × 1.2
★ Downhill, Steep: As above, × 1.05
★ Rolling hills: As Above, × 0.8
★ Steep Hills: As Above × 0.6
★ Mountain Pass: As Above, × 0.3
★ Mountains Otherwise: As above, × 0.1
Working Average: = 0.75 × 0.9 = × 0.675
I have to emphasize that these are approximate values; Chapter 5 will go into a lot more detail on the subject. For that reason, don’t be afraid to round off more savagely than I’ve done; for the purposes of this chapter, 2 significant digits is almost certainly accurate enough. I generally use 2-4 decimal places out of force of habit, but it really is overkill – but not worth going back through what I’ve already written (both above and below) to correct..
Stride length is proportionate to leg length, which – for human anatomical purposes – is proportional to overall height. More or less.
★ So, for non-humans / unusual humans: × Ht(‘) / 5’ or × Leg Length(‘) / 2.4’
★ Multiply everything × the basic pace, multiply by the Encumbered movement rate / 30′, and multiply × 4.
★ Then, all you have to factor in any rest requirements, as described earlier.
The Hero System is a bit more complicated, but it’s all simply a matter of making the adjustments necessary, one at a time.
Base Movement rate is 2″ = 4m per round. A round is 12 segments divided by the character’s Speed, which is usually 1, 2, or 3 – nothing faster qualifies as ‘normal human’. 2 is the normal human standard, so that’s 12/2=6 rounds in a 12-segment turn, or 6x6x60 = 2160 in an hour.
There are 2160 segments in an hour, so that’s 8.64 km an hour, or 5.37 mph. But that’s for a normal walk – even if we assume the default character falls into the ‘high fitness’ category (which we shouldn’t do), that’s just a little faster than it should be.
Never mind, take the character’s movement rate and multiply by 0.9311 to correct for this. Hours, minutes, and seconds remain the same in both systems, so all we need from there is to be able to convert the movement rate is to go from mph to km/h and back:
★ 1 mph = 1.61 km/h
★ 1 km/h = 0.621 mph
★ 1 mile = 1.61 km
★ 1 km = 0.621 miles
Humans need between 1 and 2 kg (2.2 – 4.4 lb) of food each day, on average. All sorts of factors can influence this value – the weight of the individual being one of them, and the volume occupied by the individual being another. These come to matter a great deal when considering non-humans with different body shapes.
Exercise or heavy work increases the need as well, by up to 50%.
Another major factor is the nutrition factor of the food – the above is based on modern nutrition, which means that you could potentially slice 25% out simply by consuming a more balanced diet; some of it is empty calories. Back in medieval times, they had far less knowledge, and since that’s the time period most fantasy is based on, the same will be true of most Fantasy Games, and that means a slight increase in the size of the recommended dietary intake – up maybe 20%.
The preservation methods that they used were not the best at preserving nutritional value. That’s maybe another 25% on top.
Taking everything into account, then, we get × 1.5 × 1.2 × 1.25 = × 2.25.
That’s 2.25 – 4.5 kg of food per day (5 – 10lb).
There are three ways to get that food: either you gather it / hunt for it yourself as you go, trading time for it; or you buy it as you go, trading money for it; or you carry it with you, sacrificing cargo capacity for it. There is no fourth option.
Humans can go several weeks without food if they have to – but they will become weak in 30-50 days and die in 43-70 days. But if you expect your employees to do without for long periods, you won’t have employees for very long.
Humans need 2 to 3 liters of water (4.227 – 6.34 pints) every day. This also goes up with exertion – to the upper value stated. And one liter of water is roughly 1 kg, or 2.2 pounds.
Humans can only go 2-5 days without water, with 3 being the usual guideline. As usual, many factors come into this estimate; exertion shortens it, as do high external temperatures. Altitude is thought by some to have a similar effect to rising temperature, based on equating heart rates to the level of exertion.
Having too much water is usually a self-correcting problem. A bigger question, always, is how much of it you need to carry? The answer is not straightforward.
As an abstract thought experiment, let’s define the probability of finding potable water in a given terrain type as the “Terrain Factor”.
★ 1. 100 / Terrain Factor gives Miles to 100% chance of replenishment.
★ 2. Divide by Speed, allowing for rest breaks, to get hours to probable replenishment.
★ 3. Divide by the number of working hours in the day to get the number of replenishments per day.
★ 4. Multiply by Daily requirements, allowing for workload to get the amount needed to reach the next replenishment point..
★ 5. Finally, allow a safety margin – some think this should be +50%, some think it should be +100%. Personally, I set the safety margin based on the confidence in the initial terrain factor – if it’s nearly certain to be accurate, you can get away with a smaller margin. If it’s nearly certain to be inaccurate, you need more margin.
Let’s run one or two quick examples:
Terrain Factor = 5% per mile
100 / 5 = 20 miles to 100%.
20 miles / 4 mph = 5 hours.
5 / 8 = 0.625.
3 liters × 0.625 = 1.875 liters.
+75% safety margin (fairly high uncertainty) = 3.75 liters.
That’s a little more than your daily needs. Even with high uncertainty, the high Terrain Factor compensates.
Terrain Factor = 8% per mile (Mountains).
100 / 8 = 12.5 miles to 100%.
12.5 miles / 1.5 mph (slow) = 8.333 hrs.
8.333 / 8 = 1..0417
3 liters × 1.0417 = 3.1251 liters.
+100% safety margin (very high uncertainty) = 6.25 liters.
That’s 6.25 kg of water, or more than 2 days supply.
The increase in terrain factor might not seem much, but it’s plenty to compensate for the slow speed..
Terrain Factor = 0.05% per mile (arid).
100 / 0.05 = 2000 miles to 100%.
2000 / 2 mph = 1000 hours.
1000 / 12 = 83.33 days.
5 liters × 83.33 days = 416.65 liters.
+100% safety margin (more than needed, but given the needs and environment, it’s justified) = 833.3 liters.
That’s 833.3 kg. Only the strongest will have any sort of Cargo capacity remaining.
The last result is VERY sensitive to the speed value. Even an additional 0.5 mph makes a significant difference:
2000 / 2.5 mph = 800 hours.
800 / 12 = 66.7 days.
5 liters × 66.7 days = 333.3 liters.
+100% safety margin (more than needed, but given the needs and environment, it’s justified) = 666.7 liters.
That’s 166.67 kg less water that has to be carried.
On top of that, water has to be contained in something, and that something has to be strong enough to hold it – when there’s a lot of it, that’s a lot of extra weight. Let’s call 1 barrel as equal to a 44-gallon drum (simply because most people will know how big the latter is) – 666.7 liters is Four of them (plus 2 cups, i.e. a small wine-skin). Per person. And the only compensation for evaporation is the safety margin.
An empty barrel of 50-gallon size weighs in at 50lb, empty. So that’s roughly another 200 lb on top of the weight of the water.
I always measure water requirements in liters, because 1 liter of water is almost exactly 1 kg, and that’s incredibly convenient. But for the non-metric game systems, you will then need some conversions.
★ 1 liter = 2.1135 pints.
★ 1 pint = 0.473 liters.
★ 1 kg = 2.2 lb
★ 1 lb = 0.454 kg.
There is also a truism that anyone who fails to completely replenish their water supply every time they have the opportunity deserves to be without. I think that’s a little harsh but contains more truth than fiction. Remember, too much water is a self-correcting problem.
These requirements add up quite quickly. If you have to cover 100 miles to reach your destination, at 3 mph, and traveling only 8 hours a day, that’s 4.17 days of food and water.
Sure, you can take it all with you – call it 3.5 × 4.167 = 14.6 kg (32 lb) of food, plus 3 × 4.167 = 12.5 kg (27.5 lb) of water, plus 5 lb or so in containers, or 29.32 kg (64.5 lb) in total, and that’s a journey under fairly favorable conditions.
And that’s for a human – the requirements increase with volume and weight. A creature 4 × human height would need between 16 and 32 times the food and water of a human. Call it 25x for convenience.
The Rocky Mountains are between 70 and 300 miles wide. At 1.5 mph, it would take 46.7 – 200 hours to cross them. At 8 working hours a day, that’s 5.8375 – 25 days. The lower number isn’t that much worse than the favorable conditions example discussed above – 41 kg (90.3 lb) will see you through. The same can’t be said of the other extreme – 175.6 kg (386.3 lb) is a significant total.
The mountains nearest to me are Australia’s Great Dividing Range, and they are between 100 and 190 miles wide. Not as extreme as the Rockies but a much more consistent width.
The Andes vary from 124 to 435 miles wide. The Alps are a very consistent 200-210 miles wide. The Pyrenees has an average width of 120 miles, but at one end they are only 6 miles wide and in the middle, 80 miles wide. The Himalayas are 125-250 miles wide, and extremely variable in width throughout their length. What’s more, they are so steep that the 1.5 mph average used above would be much lower – 0.15 mph in places! – so they are the equivalent of 100 times their width in terms of crossing them.
If you’re lucky enough, there may be villages and inns along the way where you can replenish supplies – this not only reduces the amount that you need to carry, but reduces the uncertainty massively.
But it’s nearly certain that in areas with unfavorable conditions, there will be no such convenience available – and that means foraging and hunting for resources as you go, simply to reduce the amount that you have to carry.
If you aren’t fussy, there’s almost certainly plenty of food out there – Orcs have a huge advantage in that respect – but almost every other species has less tolerance. Hunting or Foraging reduces travel speed 25%, doing both drops it to 56%.
One alternative is to dedicate 1/4 or more of the working day to these pursuits instead of using them to travel. 1/3 is a convenient number because the typical day can then be broken down as follows:
★ 1 hr eat, break camp
★ 8 hours travel
★ 4 hours hunting / foraging
★ 1 hr eat, set up camp
★ total = 14 hours
Why is that convenient? Except at or near the equator, you can count on roughly 14 hours of sunlight in summer. Today, for example, is going to be 14 hrs 16 minutes long, here in Sydney. In New York City, it’s currently Winter, so there will be only 9 hrs 25 minutes of daylight – and hunting / foraging would arguably take longer because of the season, maybe as much as 5-6 hours. So the time available for travel goes down 14-9.5=4.5 hrs for daylight and 1-2 hrs for slower hunting to just 1.5-2.5 hrs. You could possibly cut the top-and-tail of the day to 30 minutes or so, restoring another hour of travel – but even before any environmental impacts on progress, it has been slowed by more than half. Instead of average 3-4 mph, 2.5 would seem more likely – and for less than half the time, so that’s under 1.25 mph over the entire working day. The only good news is that snow becomes water fairly easily, all you need is a fire and something to put the water in until it melts.
For comparison:
Stockholm: 6 hrs 37 min of daylight
Berlin: 8 hrs of daylight
Madrid: 9 hrs 31 minutes of daylight
London: 9 hrs 34 minutes of daylight
Orlando Florida: About 10.5 hrs of sunshine
Cairo: 11 hrs 21 min of daylight
Johannesburg, South Africa: 13h 40m daylight
Auckland, New Zealand: 14 hrs 30 min daylight
Hobart, Tasmania (Australia): 15 hrs 15 min daylight.
At long last, we’ve pruned the time down to what’s really available, and adjusted the speed to what’s possible. As stated, Speed × Time gives distance, and that defines time.
More precisely, the distance from A to B defines how many working days it takes to cross that distance, and that determines spoilage and expenses and therefore profits.
Outside of using it to translate one of those into the other, Speed is actually irrelevant.
Let’s start with the human bottom line, and work outwards. The human advantage means that if Cargo Weight doesn’t incur an Encumbrance penalty, they can be the most efficient form of delivery service (with exceptions that I’ll cover in subsequent sections).
As soon as a human needs to spend time hunting / foraging, especially for water, their efficiency declines massively. In summer months, extended daylight hours can compensate for this to some extent.
Significant armor of any sort compromises Cargo Carrying Capacity, however. If there are significant dangers on the road (and it wouldn’t be a real Fantasy campaign if there were not, at least in some parts), that rules humans out as an efficient mechanism for freight transport.
In fact, if anything compromises the ideal situation, some other solution is almost certain to be more efficient. But, under the most perfect of circumstances, they can be hard to beat.
Elves are just a little less efficient under most circumstances than humans. Working in their advantage is their nimbleness of foot, which can more than compensate under certain circumstances – sandy deserts and deep snow being the most obvious, because these conditions greatly compromise human movement. An ideal situation might seem to be using humans in Warmer months and Elves in Colder months, but to retain each workforce with any certainty, they would have to be employed year-round – and that is even more compromising than either race’s shortcomings as beasts of burden.
With a lot of finesse and planning, that can perhaps be overcome. It would mean stationing the humans in designated locations to assist in loading and unloading, sales, etc, during the winter months, and replacing them with the Elves in the warmer months. But doubling any workforce when you don’t double your income is not a recipe for business security, so even this might be problematic.
On top of all that, there’s the personality factor: unless forced to it, I can’t imagine many elves who would be happy carrying Cargo from one place to another. Again, there might be rare exceptions for certain Cargoes, but overall – no.
Dwarves have advantages even over humans – but they are limited by their habit of wearing heavy armor, especially anytime they have to leave the relative security of their tunnels. In that environment, where their smaller size provides an added advantage, they can’t be beat; which generally means that trading with Dwarves tends to take place at the entrances to their domains.
On top of that, Dwarves tend to be as stiff-necked about menial labor as Elves. Note that they don’t consider mining and related activities to be “Menial”.
Halflings are compromised by size and speed. But they can be workhorses if used in the right way – and they are willing. One big advantage is that they need less food and water than a human – but good luck ever getting one to admit that.
Larger Orcs are genuine rivals to humans. Their size counts against them (greater food requirement for little gain in STR), but their capacities are higher, and they are generally more willing to undertake “menial” tasks – for the right rewards. As noted above, though, their biggest asset is their tolerance for tainted / rotten meat; food that would be intolerable to a human is perfectly acceptable to an Orc.
The combination tends to mean that Orcs are naturally valuable as slaves, and if this is not to be a feature of a campaign, the GM needs to explicitly consider why it is not the case. My go-to explanation has always been that Orcs will swear blood feuds against those who enslave their kind – eternal enmity, even if the captives are liberated / freed. Just another brick to be emplaced in the world-building wall…
Ogres have a large Cargo Capacity and relatively high STR for their size. Compromising this is their food requirements, which will be about eight times human – by the time that is taken into account, they are actually less efficient than Humans. On top of that they do NOT get the Human Advantage, even in watered-down form.
Bugbears can make great Forklifts – if they are civilized enough, or can be forced into it. Especially if you use my modification (STR 15-23) instead of the standard STR 15. They are close enough to human size that their food requirements are relatively easily met (about × 3.5 human), and their musculature particularly favors point loads. Comparing with a STR 11 human:- 115 lb base Carrying Capacity, × 3.5 = 403 lb, / 1.25 = 322 lb, /2/1.5 (Size, Proportions) = 107lb, gives STR 13. so a Bugbear of STR 13 is as efficient as a human – if the Human Advantage isn’t taken into account. STR 15+, and the point-load advantage, more than compensates for that advantage in the eyes of some.
Acting to restore the balance is willfulness and laziness. So they can be more effective than humans – but won’t be.
Size counts heavily against them, but they tend to be very strong. With a balanced load, they can more than hold their own – at least until that is taken into account. Tipping the balance one way is their natural regenerative abilities, tipping it the other way is the Human Advantage (which trolls don’t share). If large game is plentiful, Trolls may make effective beasts of burden – but they won’t be much better in the long run than a human.
Size is an even worse factor here – a small Hill Giant probably consumes 5-6 × a normal human diet, a large one 75-85 × a normal human. Both varieties have large Capacity adjustments in their favor but in the case of the larger Hill Giants, that’s not enough to compensate for these needs.
.
Stronger than a Large Hill Giant but with the load capacity adjustment of a small one, these are not as Efficient (when all is said and done) as a Hill Giant. Throw in some significant armor (are you going to take it off him?) and there’s no real contest.
Size goes up faster than STR. And food requirements go up geometrically with size. Sure, they can carry a lot – but not enough, except in very specific circumstances. The ability to pick up a heavy load and wade across a bay or shallow sea would make them competitive with humans loading and then unloading a ship, for example. But there might need to be several such loads a day to justify employing one for the purpose.
The same is generally true of most other humanoids. They are either small-size-and-STR compromised, or they are large-size, incurring a disproportionate dietary burden as a result. While there may be specific circumstances in which they can compete with a human, overall, ordinary humans remain the standard to measure against.
3.1.2 Horses as a beast of burden
The following has been excerpted from Adventurer’s Club #32, “The Hidden City”:
★ Horse bodyweight = 1800lb
★ Carry 360 lb = 160 kg safely, carry 360 × 2= 720kg max load
★ 7.5 gallons per day fresh water= 28.4 kg + containers = 35 kg/day
★ The average 1000 pound horse must eat approximately 10 to 20 pounds of hay or forage every day, or about 1-2% of their body weight. The usual recommended amount is 1.7%.
★ 1.7% of 1000 pounds = 17 lb = 7.72kg.
★ They will naturally supplement this with forage. They have a greater tolerance for lush greenery than mules but can develop cholic if they overindulge.
★ Horses can go only 2 days without water but can go almost a month without food. This only saves 14kg a day, but every 2½ days without food adds 1 day’s water (28+7=35) to their capacity. Safety suggests no more than 2 weeks on this regimen. This can be extended if suitable forage is available.
★ Assume 2 kg dead weight
★ Consumables total 49 kg / day
★ (2 × horses carry 1440 kg, but will need additional supplies for the second animal).
Horses are superbly optimized for what they do well – which does not include carrying a rider, believe it or not. The weight of the rider is located at the middle of their back, and while Horses have strong spines, there are limits, which a ride bouncing up and down when the horse is at speed can sometimes exceed.
In fact, part of the purpose of a saddle is t o spread the rider’s weight over a larger area on the horse’s back.
In some ways, horses are very intelligent, and in others, they are as dumb as posts. Quite often, for example they learn to defer to the judgment of their rider, even if the horse considers a situation risky. As a general rule, they are reluctant to exceed the speed they consider safe, given the terrain – but they never look ahead or anticipate by very much; they live entirely in the ‘now’. They will keep going in their direction of travel until the good ground gives out, even if they could clearly see that the ground a short distance ahead is unstable. “I’ll worry about that when I get there, it may have changed by then,” seems to be the thought in their heads. For the same reason, they will approach a jump with total confidence – only to lose their nerve at the last second.
They can (and do) learn human voice commands – the tone of voice is very important, as is familiarity with the rider. Put the two together, and the rider isn’t just instructing the horse what to do, they are telling the horse, “I’m in charge, you can trust me.”
I was watching the Olympics Show-jumping or Dressage or some such (not something I usually do, but it was the most interesting thing available), while at the same time working on something else. The commentary started to discuss how each gait had a different leg movement pattern, and how most horses couldn’t go from one to another without taking at least one step in an intermediate gait, and the intelligence of horses, and how the secret to getting a horse to perform a difficult jump was to convince it that it could succeed – a psychological question. A horse and rider who were in sync on the day could outperform another pair who may have been the strongest – on paper – for that reason.
If confronted with a danger, a horse’s first reaction is to run away from it. Finally, horses do not naturally back up – they are more likely to rear up and twist during the descent to start to turn away, or simply turn to one side. Some clever work with block and tackle is therefore needed when using them to belay a load down a steep incline.
Horses can move very quickly at full gallop, but can’t carry very much weight when doing so. Their speed declines faster than their carrying capacity increases – especially if they are also carrying a rider. If led, they can carry a fair amount, because they are not required to deliver speed – but for the amount of food and water they require, this is not a very efficient approach.
Horses that graze in pastures typically eat in 30 to 180-minute bouts, and may eat for 10 to 12 hours a day. They may eat 112.5 grams per hour on poor grazing, 225 grams per hour on average grazing, 337.5 grams per hour on good grazing, and 450 grams per hour on excellent grazing.
Let’s put those numbers in terms of hours needed to reach the 7.72 kg for a day’s hard work: Poor grazing: 68.6 hours/day. Average grazing: 34.3 hours/day. Good grazing: 22.9 hours/day. Excellent grazing: 17.16 hours / day.
But those are misleading. The 7.72 kg is based on the horse doing something profoundly against its’ nature – working hard all day. Simply resting requires far less energy. Unfortunately, I was never able to find specific numbers.
Nevertheless, let’s see how far logic can get us.
If there are 8 working hours in a day, then 7.72 kg gets us 8 hours of work, so 1 hour of work requires 7.72 / 8 kg of fodder = 0.965 kg. There are 60 minutes in an hour, so that 0.965 kg gets us 60 minutes of work; which means that 1 minute of work requires 0.016083 kg of fodder. There are 1000 grams in a kg, so that’s 16.083 grams per minute of work – or, in other words, 0.06218 minutes of work per gram of fodder.
Now, that’s a useful number. If we multiply by the amount grazed in an hour, we get the number of minutes of work that can be sustained after that hour.
We can also reformulate these results to get the amount of work permitted every hour by that level of grazing.
Puts things into an entirely new perspective, doesn’t it?
And that smoothly segues into the primary freight operation at which they are undoubtedly the most efficient conventional solution: One rider rides a horse, hell for leather, until it can go no further – then swaps it out for a fresh mount. Changing mounts every 2-4 hours gets whatever is being carried – usually documents or information – where it’s going in the absolutely fastest time possible.
Unfortunately, there are creatures that can steal the horse’s thunder in this respect, if they are minded to. Anything with a flying speed of 30 ft or more will usually leave the pony express in the shade. The Eagles from the Hobbit come to mind, for example. And that’s before wizards start apporting things!
The bottom line for Horses is, then, that there are other creatures who are even better at their best claim to being a transport solution – but those creatures are far harder to come by and likely to charge a stiff fee for their services. Which puts horses back in the frame.
3.1.3 Burros as a beast of burden
Excerpted from the same adventure:
★ Mule bodyweight = 370-460 kg = 400 kg ave
★ Carry 80 kg safely, carry 80 × 4 = 320 kg max load
★ 4.5% bodyweight per day fresh water = 18kg / day + containers = 24kg / day
★ 1.5% bodyweight per day fodder (eating food that is too lush makes them sick (laminitis)) = 6 kg / day
★ mules have a greater tolerance for low feed levels than horses, and can work for up to 2 weeks on virtually no feed. Their digestive processes actually grow more efficient under such conditions to better utilize the available feed.
★ Assume 1 kg dead weight.
★ Consumables total 30 kg / day
★ 2x mules carry 640 kg, will need additional supplies for the second animal).
Donkeys and Mules are very different from Horses. Far more stubborn, and intelligent in ways that horses never are, they are adept at finding the safest course through difficult terrain if there is one. That said, they value their own skins far more highly than they value anything they happen to be carrying. I have heard stories (possibly apocryphal) of Burros refusing to cross particular terrain they they distrust on steep mountain passes, throwing off their rider, staring at him as he hangs off the edge of a cliff by the reins as if to say, “I told you it wasn’t safe,” and then biting through the reins to send said rider plummeting ground-ward.
If presented with uncertain footing, and not forced onto it, Donkeys and Mules will search around for an alternative route in a systematic way, skirting the edge of the unsafe terrain until they find a way forwards.
If confronted with a danger, the Mule / Donkey’s first instinct is to kick at it or stomp on it. An entire team will eagerly attempt to do this to whatever the threat is. Only if they don’t think this is going to be enough will they flee – usually turning to deliver a parting kick along the way, just to buy themselves time.
In other ways, Mules and Donkeys are less intelligent than horses – they show no regard for voice commands from any source and seem to have a limited capacity to recognize others. Or maybe they just don’t care.
Burros of all types have two absolutely huge advantages when it comes to freight: the eat things that horses won’t, and they require far less food per kg of cargo carried. They are stubborn and pig-headed and that can be turned to the advantage of a trader who is breaking new trails.
Their big drawback is that they are small and have comparatively low capacities as a result.
3.1.4 Carts as a ‘beast of burden’
There are many creatures that can pull a cart or wagon. Buffalo, Elephants, Burros, Horses, Camels – and that’s before we get exotic.
Most of these suffer from the problem of being slow. Horses and Camels (which can be thought of as Desert Horses in this context) storm back into significance in this context.
That’s because their pulling power is not impacted the way their Carrying capabilities are. So how much weight can a Cart carry?
Well, aside from the physical limitation of how much will fit, there are six major restrictions, any one of which can be the limiting factor.
Most cart axles are made of wood – steel is too heavy and too brittle, to be honest – at least in most fantasy campaigns. The thicker the axle, the stronger it will be – but the more rolling resistance it will offer. So there is a constant desire to slim the axle down to the absolute minimum.
On smooth roads, you can get away with this – but as soon as the going gets rough, the axle risks collapse.
Consider a pothole, of depth h. It takes the wheels time t to descend to the bottom of the pothole. Inertia makes the load reluctant for an instant to fall – but gravity will not be denied. So, an instant after the wheels get to the bottom of the pothole, the full load comes crashing down on the cart-bed. And this sudden distress – many times the static load being carried by the wagon – can break things.
It doesn’t have to be a pothole, either – any roughness to the surface has the same effect. A stone that lifts the wheels only for them to come crashing back down, for example.
There’s a very technical way of calculating how much the force is going to be, i.e. the effective weight of the Cargo in that instant. But it’s too complicated, too much palaver to be practical.
Instead, I use a standard measure for the roughness of the road, which defines a range of heights that will be encountered at some point along that road.
In theory, the roughness also dictates the frequency that the checks have to be made. Nah, too much die rolling. Instead, the roughness imposes a second modifier to reflect the increased chance of failing just one of the checks. By a convenient coincidence, this modifier just happens to be exactly the same as the first.
★ Grade 1: <1mm roughness: Modifier = 20 × Load Wt / Capacity
★ Grade 2: 1-2mm roughness: Modifier = 28 × Load Wt / Capacity
★ Grade 3: 2-4mm roughness: Modifier = 40 × Load Wt / Capacity
★ Grade 4: 4-8mm roughness: Modifier = 56 × Load Wt / Capacity
★ Grade 5: 8-16mm roughness: Modifier = 80 × Load Wt / Capacity
★ Grade 6: 16-32mm roughness: Modifier = 112 × Load Wt / Capacity
★ Grade 7: 32-64mm roughness: Modifier = 160 × Load Wt / Capacity
★ Grade 1: < 1/12 " roughness ★ Grade 2: 1/12" - 1/6" roughness ★ Grade 3: 1/6" - 1/3" roughness ★ Grade 4: 1/3" - 2/3" roughness ★ Grade 5: 2/3" - 1 1/3" roughness ★ Grade 6: 4/3" - 2 2/3" roughness ★ Grade 7: 8/3" - 5 1/3" roughness Modifiers as above The roughness measures high point to low point within a horizontal distance of an inch or so. Which means that has drops of half an inch would be Grade 4, while the example below - carefully scaled to 100% - has drops of an inch, and is Grade 5.
So, if a cart weighs 350 lb, and the Cargo weighs 250 lb: Grade 1 = 5000 lb; Grade 2 = 7000 lb; Grade 3 = 10,000 lb; Grade 4 = 14,000 lb; Grade 5 = 20,000 lb; Grade 6 = 28,000 lb; Grade 7 = 40,000 lb. If the Cart has a capacity of 800 lb, those are modifiers of: -6, -9, -12, -18, -24, -36, -and 48 respectively.
The wagon driver gets to roll a skill check against DC 0 (or system equivalent), i,e, add his skill, INT modifier, and a d20 roll, to the cart’s CON Modifier. This represents the driver being aware of the danger and trying to smooth the passage / steer the cart around the worst of it. Let’s say that these are 4, 4, 12, and 10, respectively, for a total of 30. Grade 1: needs 24 or less. Grade 2: needs 21 or less (on that d20 roll). Grade 3: needs 18 /-, so for the first time there is a chance of something breaking. Grade 4: needs 12 /- so approaching 50-50. Grade 5: needs 6/-, so about 75% chance of something breaking. Grade 6: cannot succeed (on this d20 roll), something breaks. Grade 7: cannot succeed (on this d20 roll), something breaks.
That something might be the axle, or a wheel, or something else – it’s up to the GM to decide where the weak point is. Depending on how it was repaired the last time something broke, it may be the same thing, or it may absolutely not be the same thing.
A cart starts with a STR of 23, enough to carry three people of 200 lb weight, drawn by a single animal of appropriate type (usually a horse or a burro), and a CON of 16.
Every +1 STR increases the capacity and also increases the CON by +1. At STR 28, 2 horses or 4 burros are needed, and the Cart has become a 4-wheeled wagon; at STR 31, this doubles again.
Each +1 STR adds 1 GP to the base price of 15 GP (D&D / Pathfinder).
Here’s the catch: Axles, Wheels, Connections, and the Carrying capacity of the cart or wagon, all have to be bought up separately. Or, to put it another way, the basic small Wagon, at 25 GP, has +10 STR and CON to distribute amongst the various attributes.
It’s usually more useful to do as is done for humanoids, and divide the load by the number of wheels. A Cart of 600 lb capacity (the minimum) therefore has a base of STR 18.
The smallest wagon (4 wheels) has a base capacity of 1200 lb / 4 wheels = 300 lbs, resetting the STR to 18, at a cost of 25 GP.
A Large wagon has a base capacity of 1800 lb / 4 wheels = 450 lbs, a STR of 21. So that’s +3 STR, costing 1+2+3=6 GP more; to get to the “Book Price” of 35 GP, there are 4 points of STR left over, distributed amongst the Axle)s, Wheels, and Connection. (In theory, it should be 36 GP, by these rules, but we’ll give the buyer a 1GP discount).
There are all sorts of things that can be done to increase STR. These either contribute to the carrying capacity or to the ability of the Wagon to withstand rough terrain – i.e. one of the three other Wagon STR stats.
Some of these add significantly to the weight of the wagon. I’ll deal with those individually as I come to them.
Every increase of 2″ diameter of the axles adds 1 STR, cumulative. The base width is 1.5″ radius, i.e. 3″ diameter. So adding 8″ to this gives a diameter of 11″, a radius of 5.5″, a cross-sectional area of 95 square inches or 13.4 times as much as the base, and a STR increase of 1+2+3+4=+10.
However, this increases weight proportionate to the increase in area (5.5^2 / 1.5^2), which shows up as +13 rolling resistance. In essence, there’s more friction and inertia to overcome.
Another option is to go with iron axles. These are a lot more expensive, about twice the weight for a given STR, but a lot smaller – 1/6 the size. So the base thickness of an iron axle is 0.25″ radius, or 0.5″ diameter, and every 1/3 of an inch diameter increase adds +1 STR.
The big advantage is that the area is a lot smaller, and so is the rolling resistance, therefore – even if the increased weight undoes some of that gain:
1.5^2 – 0.25^2 = -2.19 – so the base adjustment is -2 rolling resistance, and the 0.19 is considered lost to the added weight.
While the rules specify the effect of STR higher than the entries shown, some people don’t know how to interpret them.
Let’s say you need the Encumbrance levels for STR 34. Subtract 10 until you get to an entry on the existing table, then multiply the Encumbrance values shown by 4 for each subtraction of 10.
STR 24: 233 lb, 466lb, 700lb.
Therefore, STR 34: 233 × 4=932lb; 466 × 4=1864 lb; and 700 × 4=2800lb.
STR 44: 932 × 4=3728 lb; 1864 × 4=7456lb; and 2800 × 4=11200 lb.
For convenience, though, here’s an extended STR table (which picks up where the official one ends):
STR |
Light Load |
Medium Load |
Heavy Load |
30 |
532 lb or less |
533 – 1064 lb |
1065 – 1600 lb |
31 |
612 lb or less |
613 – 1224 lb |
1225 – 1840 lb |
32 |
692 lb or less |
693 – 1384 lb |
1385 – 2080 lb |
33 |
800 lb or less |
801 – 1600 lb |
1601 – 2400 lb |
34 |
932 lb or less |
933 – 1864 lb |
1865 – 2800 lb |
35 |
1064 lb or less |
1065 – 2132 lb |
2133 – 3200 lb |
36 |
1224 lb or less |
1225 – 2452 lb |
2453 – 3680 lb |
37 |
1384 lb or less |
1385 – 2772 lb |
2773 – 4160 lb |
38 |
1600 lb or less |
1601 – 3200 lb |
3201 – 4800 lb |
39 |
1864 lb or less |
1865 – 3732 lb |
3733 – 5600 lb |
40 |
2128 lb or less |
2129 – 42564 lb |
4257 – 6400 lb |
41 |
2496 lb or less |
2497 – 4896 lb |
4897 – 7360 lb |
42 |
2768 lb or less |
2769 – 5536 lb |
5537 – 8320 lb |
43 |
3200 lb or less |
3201 – 6400 lb |
6401 – 9600 lb |
44 |
3728 lb or less |
3729 – 7456 lb |
7457 – 11200 lb |
45 |
4256 lb or less |
4257 – 8528 lb |
8529 – 12800 lb |
46 |
4896 lb or less |
4897 – 8208 lb |
8209 – 14720 lb |
47 |
5536 lb or less |
5537 – 11088 lb |
11089 – 16640 lb |
48 |
6400 lb or less |
6401 – 12800 lb |
12801 – 19200 lb |
49 |
7456 lb or less |
7457 – 14928 lb |
14929 – 22400 lb |
+10 |
x4 |
x4 |
x40 |
Most of what you need to know about wheels is covered in the preceding sections.
Wheels come in two types of three types, with multiple subtypes.
★ Spoked, Wood
★ Spoked, Metal
★ Solid, Wood
★ Solid, Metal
Spoked wheels start with 3 spokes. You can get +1 STR by thickening those spokes:
★ T = (t+X)^2 / t^2
+1 STR per X
Wooden spokes:
★ base t = 1 inch thickness
★ X = +0.5 inches
Remember, these are spoke diameters, but arranging things this way also accommodates spokes of different shapes.
You can double one axis by halving another – so instead of spokes 2″ radius, you could have spokes 1″ thick and 4″ wide. Spokes have an upper limit of 4.5″ – 5″ wide, so there are limits. Also, any spoke less than 0.25″ thick is likely to break heavy loads with fairly routine shock. In fact, that’s a risk with anything less than an inch thick; you can get away with it in the case of vehicles designed to carry minimal weight, like a chariot (no cargo capacity to put the spokes under extreme stress).
Metal spokes:
★ base t = 0.5″
★ X = 0.2″
Metal spokes are less likely to break, but are prone to bend. This introduces a weakness into the metal even if the problem is repaired; it will eventually fail again under heavy load. Cast Iron is usually the exception; it fractures instead.
Bronze spokes are +4 STR relative to wood. (Cast) Iron spokes are +4 STR relative to Bronze. Steel spokes are +4 STR relative to Iron. Adamantine spokes or other exotic alloys may be +4 STR relative to Steel, that’s up to the GM.
Spokes start at 1/2 GP each (wood) and each material improvement costs more than the equivalent STR in the previous material. They increase in price as they get better, of course, and the rate of increase also accelerates.
Let’s put all that in a set of tables:
#X |
Wooden Wheels |
|||
Size |
Alternative |
STR |
Price |
|
0 |
0.5 |
1″ × 0.25″ |
10 |
0.5 |
1 |
0.75 |
1.5″ × 0.38″ |
11 |
1 |
2 |
1 |
4″ × 0.25″ |
12 |
1.5 |
3 |
1.25 |
1.57″ × 1″ |
13 |
2 |
4 |
1.5 |
4.5″ × 0.5″ |
14 |
2.5 |
5 |
1.75 |
4.1″ × 0.75″ |
15 |
3.5 |
6 |
2 |
4″ × 1″ |
16 |
4.5 |
7 |
2.25 |
4.5″ × 1.13″ |
17 |
6 |
8 |
2.5 |
4.5″ × 1.4″ |
18 |
7.5 |
9 |
2.75 |
4.5″ × 1.7″ |
19 |
9.5 |
10 |
3 |
4.5″ × 2″ |
20 |
12 |
#X |
Bronze Wheels |
|||
Size |
Alternative |
STR |
Price |
|
0 |
0.25 |
0.5″ × 0.125″ |
14 |
7.5 |
1 |
0.45 |
0.81″ × 0.25″ |
15 |
9.5 |
2 |
0.65 |
1.69″ × 0.25″ |
16 |
11.5 |
3 |
0.85 |
1.7″ × 0.43″ |
17 |
13.5 |
4 |
1.05 |
2.8″ × 0.4″ |
18 |
15.5 |
5 |
1.25 |
1.57″ × 1″ |
19 |
18 |
6 |
1.45 |
4.21″ × 0.5″ |
20 |
20.5 |
7 |
1.65 |
5.45″ × 0.5″ |
21 |
23.5 |
8 |
1.85 |
4.9″ × 0.7″ |
22 |
26.5 |
9 |
2.05 |
4.21″ × 1″ |
23 |
30 |
10 |
2.25 |
4.5″ × 1.13″ |
24 |
34 |
#X |
Cast Iron Wheels |
|||
Size |
Alternative |
STR |
Price |
|
0 |
0.25 |
As Bronze |
18 |
46.5 |
1 |
0.45 |
As Bronze |
19 |
49.5 |
2 |
0.65 |
As Bronze |
20 |
53 |
3 |
0.85 |
As Bronze |
21 |
56 |
4 |
1.05 |
As Bronze |
22 |
60 |
5 |
1.25 |
As Bronze |
23 |
64 |
6 |
1.45 |
As Bronze |
24 |
68 |
7 |
1.65 |
As Bronze |
25 |
73 |
8 |
1.85 |
As Bronze |
26 |
78 |
9 |
2.05 |
As Bronze |
27 |
84 |
10 |
2.25 |
As Bronze |
28 |
90 |
#X |
Steel Wheels |
|||
Size |
Alternative |
STR |
Price |
|
0 |
0.25 |
As Bronze |
22 |
180 |
1 |
0.45 |
As Bronze |
23 |
184 |
2 |
0.65 |
As Bronze |
24 |
188 |
3 |
0.85 |
As Bronze |
25 |
192 |
4 |
1.05 |
As Bronze |
26 |
197 |
5 |
1.25 |
As Bronze |
27 |
202 |
6 |
1.45 |
As Bronze |
28 |
208 |
7 |
1.65 |
As Bronze |
29 |
214 |
8 |
1.85 |
As Bronze |
30 |
220 |
9 |
2.05 |
As Bronze |
31 |
227 |
10 |
2.25 |
As Bronze |
32 |
234 |
#X |
Adamantine / Exotic Alloy Wheels |
|||
Size |
Alternative |
STR |
Price |
|
0 |
0.25 |
As Bronze |
26 |
1085 |
1 |
0.45 |
As Bronze |
27 |
1091 |
2 |
0.65 |
As Bronze |
28 |
1097 |
3 |
0.85 |
As Bronze |
29 |
1103 |
4 |
1.05 |
As Bronze |
30 |
1110 |
5 |
1.25 |
As Bronze |
31 |
1117 |
6 |
1.45 |
As Bronze |
32 |
1125 |
7 |
1.65 |
As Bronze |
33 |
1135 |
8 |
1.85 |
As Bronze |
34 |
1145 |
9 |
2.05 |
As Bronze |
35 |
1165 |
10 |
2.25 |
As Bronze |
36 |
1200 |
You may be wondering why anyone would bother not going up to the more expensive materials. The top wooden spokes confer a STR of 20 and cost 12 GP each. The same STR in Bronze spokes costs 20.5gp. In Cast Iron, just 53 GP each. So the cost is part of the reason.
Another part is that they are heavier, increasing the rolling resistance by the increase in Strength, and part of the answer is that replacements become progressively harder to obtain and repairs more expensive the further down the list of materials you go. It’s relatively easy to get a broken wooden spoke replaced; it’s rare to find anyone competent to make a steel one. The tools available in a pre-industrialized society simply don’t have the accuracy needed, and the people (in general) don’t have the necessary skill, and there are always more profitable things to do with the resources (like armor).
Increasing the size of the spokes is not the only way to increase the strength of a wheel. You can also increase the number of spokes – if there’s room on the hub.
★ Hub Radius = Axle Radius = Spoke Width × N / (2 π)
I had designed another table to show the effect on STR and Cost respectively but it became unwieldy because of the number of entries that were going to be required. So, instead, I’ve distilled it down to a cheat-sheet table.
★ 1. Write the Price of the spokes you’re using on a line.
★ 2. Underneath, write the number of spokes in square brackets like this [6].
★ 3. Draw a horizontal line under the square brackets the width of the first number.
★ 4. For each digit, look up the corresponding number on the table and write the result underneath the digit.
★ 5. Draw another horizontal line.
★ 6. Add up the digits in between the horizontal lines.
★ 7. This is the price per spoke, so multiply by the number of spokes to get the total for the whole wheel.
★ STR = +2 per step across the Number Of Spokes table, below.
★ Rolling Resistance penalty = -1 per step across the Number Of Spokes table, below.
Base |
Number of Spokes |
||||||||
4 |
5 |
6 |
7 |
8 |
9 |
10 |
12 |
16 |
|
1 |
1.33 |
1.67 |
2 |
2.33 |
2.67 |
3 |
3.33 |
4 |
5.33 |
2 |
2.67 |
3.33 |
4 |
4.67 |
5.33 |
6 |
6.67 |
8 |
10.67 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
12 |
16 |
4 |
5.33 |
6.67 |
8 |
9.33 |
10.67 |
12 |
13.33 |
16 |
21.33 |
5 |
6.67 |
8.33 |
10 |
11.67 |
13.33 |
15 |
16.67 |
20 |
26.67 |
6 |
8 |
10 |
12 |
14.33 |
16 |
18 |
20 |
24 |
32 |
7 |
9.33 |
11.16 |
14 |
16.33 |
18.67 |
21 |
23.33 |
28 |
37.33 |
8 |
10.67 |
13.33 |
16 |
18.67 |
21.33 |
24 |
26.67 |
32 |
42.67 |
9 |
12 |
15 |
18 |
21 |
24 |
27 |
30 |
36 |
48 |
Let’s do a quick example:
STR 24 Iron Spokes, 1.45″ radius, cost / spoke 68. Replacing the base 3-spoke design with a 6-spoke arrangement.
Hub Radius = Axle Radius = Spoke Width × N / 2 π) = 1.45 × 6 / (2 × 3.1415927) = 1.38465″ or greater. Call it 1.4″ radius.
3 additional spokes = +6 STR, -6 Rolling Resistance.
1. Write the price: 68
2. Write the number of spokes in square brackets: [6]
3. Draw a line: —————————-
4a. Look up “8” and “6 spokes” on the table.
4b. Write the result, “16”, on a line with the “6” under the “8”.
4c. The next digit is a 6. Look up “6” and “6 spokes”.
4d. Write the result, “12”, with the 2 under the 6..
5. Draw another line.
6. Add up the columns of numbers. I get 136 GP per spoke.
NB: Keep the decimal point position under where it was in the original price.
That’s 816 GP per wheel.
Achieving that +6 STR could be done by going to slightly thicker spokes made of steel – at a cost of 220 GP per spoke, or 660 GP per wheel.
Of course, the biggest advantage of multiple spokes is that even if one breaks and the wheel deforms, bends, or breaks, it’s more likely to still be usable – at least for a while.
★ 3 spokes, -1, is trouble and going nowhere.
★ 4 spokes, -1 isn’t a whole lot better – crippling at best.
★ 5 spokes, -1, would not be a comfortable ride, but you might manage – for a while.
★ 5 spokes, -2 adjacent, would be going nowhere.
★ 6 spokes, -1, would be similar to 5-1.
★ 6 spokes, -2 adjacent, is the same as 4-1.
★ 7 spokes, -1, would also not be dissimilar to 5-1.
★ 7 spokes, -2 adjacent, would be similar to 5-1 or 6-1.
★ 7 spokes, -3 adjacent, would be as disastrous as 3-1.
★ 8 spokes, -1, would produce a little side-to-side rocking.
★ 8 spokes, -2 adjacent, would also not be dissimilar to 5-1.
★ 8 spokes, -3 adjacent, is the same as 4-1.
★ 9 spokes, -1, would be barely noticeable.
★ 9 spokes, -2, would be similar to 7-1 if the missing spokes were adjacent.
★ 9 spokes, -3 adjacent, would also not be dissimilar to 5-1.
★ 9 spokes, -4 adjacent, would be as crippling as 4-1.
★ 9 spokes, -5 adjacent, would be as disastrous as 3-1.
★ 10 spokes, -1, would be barely noticeable.
★ 10 spokes, -2, would be similar to 9-1 if the missing spokes were adjacent.
★ 10 spokes, -3, is the same as 4-1 if the missing spokes were adjacent.
★ 10 spokes, -4 adjacent, would be as bad as 3-1.
★ 12 spokes, -1, would be barely noticeable.
★ 12 spokes, -2 adjacent, would be the same as 6-1.
★ 12 spokes, -3 adjacent, would be the same as 4-1.
★ 12 spokes, -4 adjacent, would be as bad as 3-1.
★ 16 spokes (not shown), -1, would not be noticeable.
★ 16 spokes (not shown), -2 adjacent, would be about the same as 12-1.
★ 16 spokes (not shown), -3 adjacent, would be the same as 9-1 or 10-1.
★ 16 spokes (not shown), -4 adjacent, would be the same as 8-1.
★ 16 spokes (not shown), -5 adjacent, would be about the same as 5-1.
★ 16 spokes (not shown), -6 adjacent, would be as bad as 4-1.
★ 16 spokes (not shown), -7 adjacent is what it takes to cripple this most expensive design.
Solid wheels are easier to make than spoked wheels. But they weigh a lot more.
It’s possible to work out how much more – the formula is T × (r-a) / (N × spoke width) to get a multiplier which can applied to the weight of a spoked wheel – but who cares about that?
(r-a) / (N × spoke width)
where
T = the thickness of the wheel (NOT the rims);
r = radius of the wheel;
a = radius of the axle / hub;
N is the number of spokes; and
spoke width should be obvious.
What we actually care about is the impact on Rolling Resistance – and for that, we can take a shortcut.
Assuming Base T = 1/2 spoke width, subtract 2 from the STR of the spoked wheel per spoke after the first, and add 50% to the result to get the rolling resistance effect. If the thickness is less than this (and it will almost certainly be so), multiply the result by the actual thickness and divide by the base thickness. Round down.
Example: Let’s use the 6-spoked wheel we just worked out: Spokes = radius 1.45″, so base T = 0.725″; STR 24+6=30. Rolling resistance 30-(2 × 5)=20; 20 × 1.5 = 30 – at 0.725″ thickness. Actual thickness – let’s say 2/5th of an inch (0.4″). 30 × 0.4 / 0.725 = 16.55. So a solid wheel of this thickness, instead of rolling resistance -6, would have -16.
Note that 2/5 of an inch is a solid plate of steel. It’s not likely to bend, and should have no problem supporting the wagon. Even 1/5th would be enough unless badly-treated by rough roads – but those are conditions it might very well be exposed to.
This is often the weak point of the whole thing – whatever joins the wheel to the axle, usually some kind of hub secured to the wheel with bolts or pegs.
Three things put these connections under greater strain than usual – roads and paths that are angled from one side to the other, turning corners, and the shearing force caused by bumps in the surface being traversed.
Combinations of two or more of these are worse still, and the triple-whammy of all three creates the most likely failure of these connections. The wheel comes off, and the cart or wagon suddenly assumes a very steep angle with reference to the horizontal; cargo will often spill out, and (depending on what it is) can be damaged or lost.
Slippery, muddy conditions and overloads make all of the above worse. Essentially, any sideways movement has to be completely contained by the connection, or one or both wheels will sheer off.
Consider the diagram below:
The top image shows the basic components of a wheel assembly. Specifics may vary – for example, the bolts might be on the inside with the thread protruding out. I’ve deliberately exaggerated the thickness so that the components are more easily seen and understood.
The second image shows what happens on a slope; the force of gravity pulls the wagon and load to one side. The same thing happens in the opposite direction to a fast turn, but wagon drivers know that and (generally) slow to reduce the effect – unless being pursued!
The third diagram shows the effect on the wheels, which try to twist on their hubs. The only thing holding the wheels to the wagon at this point is the strength of the thread in the connecting bolts.
Typically, this will be STR 10, at a cost of 1gp per bolt. This can be increased at a cost per bolt of 0.2 GP per bolt to a maximum of STR 25. Divide by 1.5 for Cast Iron, Divide by 3 for Bronze, divide by 5 for wooden pegs. (This applies to both STR and cost per bolt).
A wheel will normally be secured by at least three and up to ten of them – usually, one per spoke, but you can double or triple that. Each additional bolt on a wheel adds 1 to the STR of the connection.
This shows the force that the STR of the bolts has to be equal to or greater than. Obviously, without knowing the weight of both cart / wagon and load, I can’t make it much simpler.
But I can work it in the other direction: Twisting Force by angle, giving the total STR that your connections can (usually) handle for a given sideways slope.
Slope |
STR |
|||||||
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
1 |
58 |
115 |
172 |
230 |
287 |
344 |
402 |
459 |
1.5 |
39 |
77 |
115 |
153 |
192 |
230 |
268 |
306 |
2 |
29 |
58 |
86 |
115 |
144 |
172 |
201 |
230 |
2.5 |
23 |
46 |
69 |
92 |
115 |
138 |
161 |
184 |
3 |
20 |
39 |
58 |
77 |
96 |
115 |
134 |
153 |
3.5 |
17 |
33 |
50 |
66 |
82 |
99 |
115 |
132 |
4 |
15 |
29 |
44 |
58 |
72 |
87 |
101 |
115 |
4.5 |
13 |
26 |
39 |
51 |
64 |
77 |
90 |
102 |
5 |
12 |
23 |
35 |
46 |
58 |
69 |
81 |
92 |
6 |
10 |
20 |
29 |
39 |
48 |
58 |
67 |
77 |
7 |
9 |
17 |
25 |
33 |
42 |
50 |
58 |
66 |
8 |
8 |
15 |
22 |
29 |
36 |
44 |
51 |
58 |
9 |
7 |
13 |
20 |
26 |
32 |
39 |
45 |
52 |
10 |
6 |
12 |
18 |
24 |
29 |
35 |
41 |
47 |
11 |
6 |
11 |
16 |
21 |
27 |
32 |
37 |
42 |
12 |
5 |
10 |
15 |
20 |
25 |
29 |
34 |
39 |
13 |
5 |
9 |
14 |
18 |
23 |
27 |
32 |
36 |
14 |
5 |
9 |
13 |
17 |
21 |
25 |
29 |
34 |
15 |
4 |
8 |
12 |
16 |
20 |
24 |
28 |
31 |
16 |
4 |
8 |
11 |
15 |
19 |
22 |
26 |
30 |
18 |
4 |
7 |
10 |
13 |
17 |
20 |
23 |
26 |
20 |
3 |
6 |
9 |
12 |
15 |
18 |
21 |
24 |
22 |
3 |
6 |
9 |
11 |
14 |
17 |
19 |
22 |
24 |
3 |
5 |
8 |
10 |
13 |
15 |
18 |
20 |
26 |
3 |
5 |
7 |
10 |
12 |
14 |
16 |
19 |
28 |
3 |
5 |
7 |
9 |
11 |
13 |
15 |
18 |
30 |
2 |
4 |
6 |
8 |
10 |
12 |
14 |
16 |
Slope |
STR |
|||||||
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
|
1 |
516 |
573 |
631 |
688 |
745 |
803 |
860 |
917 |
1.5 |
344 |
383 |
421 |
459 |
497 |
535 |
574 |
612 |
2 |
258 |
287 |
316 |
344 |
373 |
402 |
430 |
459 |
2.5 |
207 |
230 |
253 |
276 |
299 |
321 |
344 |
367 |
3 |
172 |
192 |
211 |
230 |
249 |
268 |
287 |
306 |
3.5 |
148 |
164 |
181 |
197 |
213 |
230 |
246 |
263 |
4 |
130 |
144 |
158 |
173 |
187 |
201 |
216 |
230 |
4.5 |
115 |
128 |
141 |
153 |
166 |
179 |
192 |
204 |
5 |
104 |
115 |
127 |
138 |
150 |
161 |
173 |
184 |
6 |
87 |
96 |
106 |
115 |
125 |
134 |
144 |
154 |
7 |
74 |
83 |
91 |
99 |
107 |
115 |
124 |
132 |
8 |
65 |
72 |
80 |
87 |
94 |
101 |
108 |
115 |
9 |
58 |
64 |
71 |
77 |
84 |
90 |
96 |
103 |
10 |
52 |
58 |
64 |
70 |
75 |
81 |
87 |
93 |
11 |
48 |
53 |
58 |
63 |
69 |
74 |
79 |
84 |
12 |
44 |
49 |
53 |
58 |
63 |
68 |
73 |
77 |
13 |
41 |
45 |
49 |
54 |
58 |
63 |
67 |
72 |
14 |
38 |
42 |
46 |
50 |
54 |
58 |
63 |
67 |
15 |
35 |
39 |
43 |
47 |
51 |
55 |
58 |
62 |
16 |
33 |
37 |
40 |
44 |
48 |
51 |
55 |
59 |
18 |
30 |
33 |
36 |
39 |
43 |
46 |
49 |
52 |
20 |
27 |
30 |
33 |
36 |
39 |
41 |
44 |
47 |
22 |
25 |
27 |
30 |
33 |
35 |
38 |
41 |
43 |
24 |
23 |
25 |
28 |
30 |
32 |
35 |
37 |
40 |
26 |
21 |
23 |
26 |
28 |
30 |
32 |
35 |
37 |
28 |
20 |
22 |
24 |
26 |
28 |
30 |
32 |
35 |
30 |
18 |
20 |
22 |
24 |
26 |
28 |
30 |
32 |
Slope |
STR |
|||||||
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
|
1 |
975 |
1032 |
1089 |
1146 |
1204 |
1261 |
1318 |
1376 |
1.5 |
650 |
688 |
726 |
765 |
803 |
841 |
879 |
917 |
2 |
488 |
516 |
545 |
574 |
602 |
631 |
660 |
688 |
2.5 |
390 |
413 |
436 |
459 |
482 |
505 |
528 |
551 |
3 |
325 |
344 |
364 |
383 |
402 |
421 |
440 |
459 |
3.5 |
279 |
295 |
312 |
328 |
344 |
361 |
377 |
394 |
4 |
244 |
259 |
273 |
287 |
302 |
316 |
330 |
345 |
4.5 |
217 |
230 |
243 |
255 |
268 |
281 |
294 |
306 |
5 |
196 |
207 |
218 |
230 |
241 |
253 |
264 |
276 |
6 |
163 |
173 |
182 |
192 |
201 |
211 |
221 |
230 |
7 |
140 |
148 |
156 |
165 |
173 |
181 |
189 |
197 |
8 |
123 |
130 |
137 |
144 |
151 |
159 |
166 |
173 |
9 |
109 |
116 |
122 |
128 |
135 |
141 |
148 |
154 |
10 |
98 |
104 |
110 |
116 |
121 |
127 |
133 |
139 |
11 |
90 |
95 |
100 |
105 |
111 |
116 |
121 |
126 |
12 |
82 |
87 |
92 |
97 |
102 |
106 |
111 |
116 |
13 |
76 |
81 |
85 |
89 |
94 |
98 |
103 |
107 |
14 |
71 |
75 |
79 |
83 |
87 |
91 |
96 |
100 |
15 |
66 |
70 |
74 |
78 |
82 |
86 |
89 |
93 |
16 |
62 |
66 |
69 |
73 |
77 |
80 |
84 |
88 |
18 |
56 |
59 |
62 |
65 |
68 |
72 |
75 |
78 |
20 |
50 |
53 |
56 |
59 |
62 |
65 |
68 |
71 |
22 |
46 |
49 |
51 |
54 |
57 |
59 |
62 |
65 |
24 |
42 |
45 |
47 |
50 |
52 |
55 |
57 |
60 |
26 |
39 |
42 |
44 |
46 |
48 |
51 |
53 |
55 |
28 |
37 |
39 |
41 |
43 |
45 |
47 |
49 |
52 |
30 |
34 |
36 |
38 |
40 |
42 |
44 |
46 |
48 |
Slope |
STR |
Slope Comparison |
|
25 |
Drop 1″ every… |
Inches Drop every 5′ |
|
1 |
1433 |
4′ 9.5″ |
1.05″ |
1.5 |
956 |
3′ 2.5″ |
1.57″ |
2 |
717 |
2′ 5″ |
2.1″ |
2.5 |
574 |
1′ 11″ |
2.62″ |
3 |
478 |
1′ 7.5″ |
3.14″ |
3.5 |
410 |
1′ 4.5″ |
3.67″ |
4 |
359 |
1′ 2.5″ |
4.2″ |
4.5 |
319 |
1′ 0.75″ |
4.72″ |
5 |
287 |
11.43″ |
5.25″ |
6 |
240 |
9.51″ |
6.31″ |
7 |
206 |
8.14″ |
7.37″ |
8 |
180 |
7.12″ |
8.43″ |
9 |
160 |
6.31″ |
9.5″ |
10 |
144 |
5.67″ |
10.58″ |
11 |
132 |
5.14″ |
11.66″ |
12 |
121 |
4.7″ |
12.75″ |
13 |
112 |
4.33″ |
13.85″ |
14 |
104 |
4.01″ |
14.96″ |
15 |
97 |
3.73″ |
16.08″ |
16 |
91 |
3.49″ |
17.2″ |
18 |
81 |
3.08″ |
19.5″ |
20 |
74 |
2.75″ |
21.84″ |
22 |
67 |
2.48″ |
24.24″ |
24 |
62 |
2.25″ |
26.71″ |
26 |
58 |
2.05″ |
29.26″ |
28 |
54 |
1.88″ |
31.9″ |
30 |
50 |
1.73″ |
34.64″ |
Since the cart-bed is what actually holds the Cargo up, this is what we initially looked at – how much the cart can “carry”.
Most carts and wagons will have four sides as well as a platform for the driver to sit on. In fancy examples, one might curve so that it forms two or more of these surfaces. The other attribute that the “bed” might have is a roof, but this tends to be fairly unusual, because it can’t be lifted to accommodate taller loads.
Another refinement would be to provide a semi-enclosed cabin for the driver, at least keeping sun and some rain off him or her.
These are all components of what people generally think of when they think “wagon” – and any of them can fail. This may or may not constitute a threat to the cargo.
Rolling resistance is the reluctance of a wagon or cart to start moving from a state of rest.
A significant portion of the rolling resistance comes from inertia, which is the reluctance of a mass to accelerate, ie to acquire speed; but that’s far from the only consideration.
The wheels have to turn. The more massive they are, the more they will be reluctant to do so. Hence, there is a contribution to rolling resistance from the wheels.
That said, the larger the radius of the wheels, the more readily they will roll, so that’s also a consideration – one that potentially outweighs the weight contribution.
Still, every little bit helps, so solid wheels are often thinner than expected and structurally reinforced by ‘ribs’ that look for all the world like spokes. These are usually only found on one side of the wheel, though.
For a wheel to turn, it needs some friction with the ground. Marshy, muddy, and ice terrains can be especially challenging in this respect (in the latter case, before ‘parking’ the cart, the driver may scatter a little bit of salt and some sand or gravel on the ice; it will melt a little and then refreeze, with a texture that makes getting underway again a little easier.
The weight of the wagon can also cause the wheels to sink into a depression if the surface is soft. This effectively adds a slope to even level ground.
For that matter, when the wagon came to a stop the previous night, there must have come a point at which the friction of the surface could not be overcome by the wagon’s remaining momentum, so there will always always be a small contributing up-slope to contend with, anyway.
The axles have to be turned by the wheels. That means overcoming the friction they have with the cart body (grease helps – even animal fat).. The thicker the axle, the greater this resistance; so there’s a contribution to rolling resistance from this source, too.
I did this graphic well in advance of writing the section on solid wheels and spokes, so the top panel is a little bit redundant, but is still correct.
The main panels are concerned with slopes. In very rare circumstances, a slope can be very helpful in overcoming rolling resistance. In fact, you can even think of Rolling Resistance as a temporary steepening of the slope in the forwards direction (that’s also important!)
Panel 3 shows a simplified view of rolling resistance as a pair of additional slopes on “virtual” ground. There’s an initial phase, when the virtual incline is steepest, and then a second phase, about twice as long, in which the resistance has been partially overcome and the vehicle is gaining momentum.
I then look at four different “real” slopes (exaggerated for the visual distinction – in reality, the “slight downslope” would generally be thought of as a steep downslope if it was at the angle shown.
First, a slight downhill – the downhill slope moderates the rolling resistance at first and then leaves the second phase effectively flat. Once full motion is achieved, it’s downhill all the way, though rolling resistance will lessen the effective gradient somewhat. With caution, no special action needs to be taken.
Second, a steeper downhill – the initial phase of the motion is effectively on flat ground, and the second phase (1/2 resistance) is slightly downhill. Once up to speed, it’s dangerously steep; wagons and carts being drawn along by animal power effectively have no brakes.
This often requires splitting an animal team up, looping a rope around a tree, and using the bulk of the team to resist the descent while only 25% of the total animal team pull the vehicle forwards. The very quick-and-dirty illustration to the left displays this procedure. Of course, the main driver is controlling the three animals – but he’s probably standing a little close to that rope. If it snaps it will whip around and could cause serious injury.
Third, I turned my attention to inclines, starting with an extremely uphill. As you can see, ‘steeply uphill’. becomes ‘extremely steeply uphill’ at first, and then moderates to different flavors of ‘Steeply Uphill’ as you get underway.
Finally, there is the more probable slightly uphill. The initial phase is effectively steeply uphill but once you get moving the steepness moderates.
This is the force that your animals have to overcome. In general, they can pull 4 × as much as they can carry, 6 × with exertion. Horses are better at it than most options, they manage 6 × quite easily. Oxen and other heavy creatures can go 8-10 times, but they tend to be slow. Each extra animal pulling adds 75% to the total (not 100%). Teams of more than 8 tend to be impractical to manage and control, and even numbers are generally preferred.
All inclines are measured (technically) as the difference in altitudes divided by the horizontal distance, called the ‘run’. But you can’t see the run, what you see is the distance up or down the slope; fortunately, the difference is small enough to be negligible unless the slope is catastrophically severe.
Railways can employ slopes of up to 60° – that’s catastrophically severe, in my book.
In Australia, 16.9° or more is extremely steep; 11.3°-16.8° is a steep road; 5.71°-11.2° is an uphill slope; 3°-5.7° or less is a moderate slope. In the US, 3% is considered the maximum for a high-speed highway, 6% the maximum for a main arterial road, and 7%-8% is tolerated in the mountains.
Cyclists have to use their own muscle power to deal with slopes, so their categories tend to be a bit more nuanced – but also probably more applicable in terms of how a team of animals pulling a cart or wagon will respond.
★ 0% (0°) is a flat road.
★ 1-3% (0.573°-1.718°) is slightly up or downhill.
★ 4-6% (2.29°-3.434°) is manageable but will cause added fatigue
★ 7-9% (4°-5.143°) is uncomfortable even for an experienced climber, and challenging for new rides.
★ 10-15% (5.71°-8.531°) is painful, even for strong, experienced, riders.
★ 16%+ (9.09°+) is very challenging even for the strongest riders.
Uphill grades of 6% increase the risk of an accident by a factor of 2.6.
Downhill grades of 6% increase the risk of an accident by a factor of 5.6!
The risks are exponential relative to the slope.
★ R = B ^ (1+S%/6)
★ where,
S is the slope (%);
B is either 2.6 or 5.6; and
R is the risk factor.
So the risk uphill doubles to 5.2 at 10.35%, and doubles again to 10.4 at 14.7%.
A 4-5% gradient is the maximum considered safe in Australia for anything but private roads, which aren’t regulated to government specifications.
The steepest road in the world is officially Baldwin St in Dunedin, New Zealand, at 34.8% (19.19°), but a number of streets elsewhere have steeper grades (they may be shorter, though).
To calculate Degrees from % gradient, use D = Arctan(% slope / 100)..
To calculate Degrees from a “1 in n” rise / fall, use D = Arctan (1/n).
Or consult the graph below:
Use these facts as and when they seem appropriate!
Sources:
1. A PDF Webinar by Austroads.com.au
Tall loads and other stacks of things have a tendency to want to, well, tip over. Especially on slopes or going around corners. It’s as though there were part of the force of gravity trying to pull the top of the load sideways – and you saw what effect that had on the wagon / cart wheels earlier.
Instead of a lot of calculations, I’ve found a graphical way of not only illustrating this, but of determining the degree of danger of the vehicle overturning.
1. Drawing a line from the top of the load to the ground, gives a distance to the base of the wagon or cart.
2. Double it because of potential swaying from side to side.
3. And then increase that to triple the original to allow for a margin of safety.
4. If the results are clearly less than 1/2 the total width of the cart, all is well (green).
5. If the results are about 1/2 the width, it’s a dangerous situation but slow down and you should be OK (yellow-orange).
6. If the results are clearly more than 1/2, then there is a danger of overturning (red).
7. If the results are more than the width of the cart / wagon, you WILL overturn at the slightest provocation (dark red).
8. If the swaying allowance is more than the width of the cart, any speed other than dead slow will overturn the vehicle (also dark red).
9. If the original is more than width of the vehicle, it HAS overturned. No question. Refer to the rightmost 15° image for an example.
This assumes more or less uniform density of the load. But everyone knows (or should know) that you put the lightest stuff on top, if you are sensible.
The last two panels show the impact of doing so and how to take this into account, and of doing it all wrong and how to handle that.
1. Divide the load into three.
2. The bottom part is always 1. The other two have their weights compared to that bottom part.
3. Do the ‘gravity arrow’ not all the way to the ground, but to the line of the next part down.
4. Multiply the length by the relative weight.
5. Add up the shortened (or lengthened) gravity vectors.
6. (If necessary) extend the line of the side of the cart/load vertically.
7. position your gravity arrow where it is the length determined above.
8. Measure the vector to the base of the cart as usual.
9. Go to Step 2 of the previous procedure and continue from there.
It sounds a lot more complicated than it is. In fact, it takes only seconds – plus the time it takes to draw a line representing the slope and a box representing the cart and load.
Compare these to the rightmost images for their respective angles with uniform loads – the lightening in the left has clearly helped, but not quite gone far enough, while the mismanagement of the load in the right has definitely made things much worse.
And that’s where I’m calling a halt to this very lengthy post! Next time: putting all of the above together, and using it all to assign a base unit for productivity, the Labor Unit. And then, I can get back to what this chapter was supposed to be all about – the faceless workers that keep a business operating!