How to Calculate Climbing Ability: The Relationship Between Torque, Total Weight and Gradient, and Why Tricycles Must Us

1. Establish a Correct Physical Model First

Climbing ability is fundamentally not a question of "how much power" but of "whether traction is sufficient". At constant speed on a gradient, required traction equals gradient resistance plus rolling resistance (aerodynamic drag is negligible at low speed):

F(N) = m × g × sinθ + m × g × cosθ × f

where m is total mass including vehicle and passengers (kg), g = 9.8, θ is the gradient angle, and f is the rolling resistance coefficient (approx. 0.015–0.03 for pneumatic tyres on hard surfaces).

Engineering practice expresses gradients as percentages: a 10% grade ≈ 5.71°, 20% ≈ 11.31°.

2. A Recalculable Example

A leisure tricycle with total weight 250kg climbing a 10% grade:

F = 250 × 9.8 × sin(5.71°) + 250 × 9.8 × cos(5.71°) × 0.02 ≈ 244N + 48.8N ≈ 293N

At a climbing speed of 6 km/h (1.67 m/s), power required at the wheel:

P = 293N × 1.67 m/s ≈ 489W

Allowing 85% motor efficiency and 96% controller efficiency, the battery side requires about 600W. This means a unit rated 500W is already at — or beyond — full load on a 10% grade at 6 km/h, and will in practice slow to 4–5 km/h. This explains the common feedback of "it's rated 800W but can't climb the community slope".

3. Why Hub Motors Struggle on Gradients: The Torque Multiplication Problem

A hub motor drives the wheel directly with no reduction gear, so the entire wheel torque must come from the motor:

Wheel torque T = F × r (r is wheel radius, commonly 0.25m)

In the example above: T = 293 × 0.25 ≈ 73Nm.

Most direct-drive hub motors have rated torque in the 20–40Nm range and can only climb by relying on short-term overload, resulting in severe heating, efficiency loss and reduced long-term life. This is precisely the technical reason for "fine on flat ground, overheats and slows on any incline".

Mid-drive motors or geared solutions multiply torque through gear ratio, allowing the same motor to deliver several times the wheel torque — but with more complex structure and higher cost. Tricycles use a different solution.

4. Why Tricycles Must Use a Differential Rear Axle

If two independent hub motors are fitted directly to the two rear wheels of a tricycle, the wheels must travel different radii in a turn (the outer wheel covers a longer path). Without a differential:

• The inner wheel is forced to slip or drag, causing rapid tyre wear;
• Steering resistance increases and low-speed turning becomes stiff;
• Body roll worsens in turns, reducing stability.

A mechanical differential allows the two wheels to rotate at different speeds while distributing motor torque between them. Hence the correct architecture for leisure tricycles and sightseeing vehicles is "single motor + differential rear axle", not "twin hub motors". This is often overlooked in selection yet directly determines durability and cornering safety.

5. Other Variables Affecting Climbing

1. Total weight: passengers, cargo bed load, canopy and battery all count; 250kg versus 400kg means a 60% difference in demand at the same gradient;
2. Tyres: under-inflation and tread wear raise rolling resistance;
3. Controller current limit: the current limit determines actual deliverable torque; rated power alone does not fully reflect it;
4. Temperature: motor and controller derate at high temperature, further reducing climbing ability;
5. Battery voltage platform: as voltage sags at low state of charge, both speed and torque drop.

6. Selection Advice for Overseas Customers

1. Provide maximum gradient, gradient length and total weight — not just "we have hills here";
2. Long climbs (over 200m) require thermal balance assessment; short climbs can rely on short-term overload;
3. For mountainous or estate projects, prefer mid-drive with reduction gearing, or differential rear axle with high-torque motor;
4. Specify controller current limit and rated/peak torque rather than comparing "power numbers" alone.