The weight the animal carries through the shafts equals the moment of the cart and load about the axle divided by the distance from axle to hitch point, so a 400 kg load on a cart with a 2 m hitch distance changes the shaft load by 20 kg for every 10 cm it moves along the bed. A 10% grade shifts it by about 15 kg, so a cart balanced for 5-10% on the flat can lift its shafts uphill and press hard downhill.
Part of Cart & Wagon Construction
Tilt and balance describe how the centre of gravity of a loaded two-wheel cart sets the pitch of the cart on its axle and the share of the weight the shafts put on the animal.
A Two-Wheel Cart Is A Lever Pivoted On Its Axle
A cart on two wheels rests on one axle. The animal holds the shafts at the other end, so the cart is a lever pivoted at the axle: whatever weight lies ahead of the axle presses the shafts down on the animal, and whatever lies behind lifts them. The carrier states the target: the load’s centre of gravity slightly ahead of the axle, so that the animal feels about 5-10% of the total load. This article derives what that means in distances, and what disturbs it.
The relation
Take distances along the bed from the axle, positive forward. Let W be the load, x_w the position of its centre of gravity, W_c the weight of the empty cart including its shafts, x_c the position of its centre of gravity, and L the distance from the axle to the point where the shafts bear on the animal. The shaft load P, downward on the animal, is the sum of the moments divided by L:
P = (W_c × x_c + W × x_w) / L
Everything below applies this one formula. Inputs are assumed round figures, chosen to show the working: W = 400 kg, W_c = 100 kg with x_c = +0.10 m (the shafts’ weight carries its centre of gravity slightly forward), and L = 2.0 m.
Where must the load sit?
Rearrange for x_w: x_w = (P × L − W_c × x_c) / W.
| Target shaft load | Operation | Load position, forward of axle |
|---|---|---|
| 20 kg (5% of 400) | (20 × 2.0 - 100 × 0.10) / 400 = 30 / 400 | 0.075 m |
| 40 kg (10% of 400) | (40 × 2.0 - 100 × 0.10) / 400 = 70 / 400 | 0.175 m |
So the load’s centre of gravity should be about 7.5-17.5 cm ahead of the axle on this cart. The target is a narrow band: Cart & Wagon Loading reaches the same kind of answer by a slightly different route.
How sensitive is it?
dP/dx_w = W / L = 400 / 2.0 = 200 kg per metre, which is 20 kg per 10 cm. Sliding the load back 10 cm, from 17.5 cm to 7.5 cm ahead of the axle, drops the shaft load from 40 kg to 20 kg. Sliding it 15 cm further back puts it 7.5 cm behind the axle, and the shaft load is (10 - 30) / 2.0 = -10 kg: the shafts now lift.
What does a slope do?
On a grade g (rise over run), the weight of the cart and load has a component along the slope, acting at the height h of their combined centre of gravity above the axle line. Going uphill that component pulls backward at height h, which turns the cart nose-up about the axle and lowers the shaft load by approximately
ΔP = (W + W_c) × h × g / L
With h = 0.6 m (an assumed centre-of-gravity height above the axle line) and g = 0.10:
- ΔP = 500 × 0.6 × 0.10 / 2.0 = 15 kg
Uphill, the shaft load falls by about 15 kg; downhill it rises by the same. A cart balanced for 20-40 kg on the flat therefore carries about 5-25 kg uphill and 35-55 kg downhill. A cart balanced near 20 kg can lift its shafts on a 20% grade (ΔP = 30 kg, so P = -10 kg). Braking does the same job: a deceleration a adds roughly (W + W_c) × h × (a/g) / L to the shaft load.
The axle-position rule
The Two-Wheel Cart article places the axle so that 55-60% of the platform lies behind it. Platform weight behind the axle lifts the shafts, not loads them, so check that rule against the moment sum above for your own bed before relying on it.
What You Need
- A tape measure and a plumb line to find the axle line
- A way to weigh the shaft tip — a spring balance or a lever (Improvised Weighing)
- The actual weights of the cart and the load, estimated or weighed (Weight Calculation & Measurement)
- Chocks and a shaft prop
Method: Set And Check The Balance
Step 1: Measure L. Measure from the axle line to the point where the shafts bear on the animal’s harness.
Step 2: Weigh the empty cart’s shaft tip with the cart level, and note the empty shaft load, P_c.
Step 3: Place the load. Put the heavy items low and at the calculated distance ahead of the axle, then lighter items ahead and above.
Step 4: Weigh the shaft tip again with the cart level, supported on a prop. The reading should be inside the 5-10% band of the load.
Step 5: Re-check after the first kilometre. Loads settle and shift, and a load that settles back 10 cm costs 20 kg at the shaft.
Common Mistakes
- Balancing for zero shaft load — the first rearward shift lifts the shafts and the animal is carried off its feet.
- Calculating on the flat only — the grade changes the load by about 15 kg per 10% for these numbers.
- Placing the weight high — a high centre of gravity multiplies the slope term and the tipping risk; see Cart & Wagon Loading.
- Forgetting the empty-cart weight — here it contributes 100 × 0.10 / 2.0 = 5 kg.
Safety
A rear-heavy cart lifts its animal, a front-heavy one drops its shafts
If the load sits behind the axle, the shafts rise and can lift the animal’s harness, and the cart tips back when it is unhitched. If it sits well ahead, unhitching drops tens of kilograms of shaft onto the ground or onto anyone near it. Chock the wheels, prop the shafts before unhitching, never pile heavy items at the tail, and never stand downhill of a loaded cart.
What’s Next
- Learn next: Cart & Wagon Loading — tipping sideways and wagon axles
- Combine with: Shafts & Hitch Points — where L is measured to