Library / Terramechanics and off-road mobility / TER-16
Terramechanics and off-road mobility
Tractive efficiency
Fraction of the wheel power that becomes useful drawbar power: the net-to-gross thrust ratio multiplied by the speed ratio (1 − s).
- Ref
- TER-16
- Rev
- v1
- Field
- Terramechanics and off-road mobility
- Result
- ηtr
DBP/H is the ratio of drawbar pull to gross thrust, and s is the driving slip. The wheel power input is H times the no-slip speed; the drawbar power output is DBP times the actual speed U = (1 − s) Re ω. Their ratio is the tractive efficiency (DBP/H)(1 − s). This simplified factorisation assumes H = Tw/Re and U = (1 − s) Re ω, and is an approximation for simplified contact models. The general definition is ηtr = DBP U / (Tw ω), using the total wheel torque and power consistently.
Fraction of the wheel power that becomes useful drawbar power: the net-to-gross thrust ratio multiplied by the speed ratio (1 − s). Both motion resistance and slip waste power.
Calculator
- Share of wheel power lost to slip, s20 %
- Share lost to motion resistance, (1 − DBP/H)(1 − s)16 %
- Share delivered as drawbar power64 %
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- With DBP/H = 0.8 and 20 % slip, the vehicle turns 64 % of the wheel power into drawbar power. Slip takes 20 % of the power, and motion resistance 16 %.
- The best slip balances two effects: more slip raises DBP/H, because it develops more thrust, but wastes the factor (1 − s). On most soils the efficiency peaks at 10 to 25 % slip, and falls to zero as the wheel spins in place (s = 1).
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| DBP/H Ratio of drawbar pull to gross thrust | 0.1 to 1 | 0.08 | 0.8 | 0.72 | +10% | +10 % |
| s Driving slip | 0 to 0.8 | 0.16 | 0.8 | 0.64 | +10% | −2.5 % |
Sweep of Driving slip
| Driving slip | Tractive efficiency |
|---|---|
| 0 | 0.8 |
| 0.1 | 0.72 |
| 0.2 | 0.64 |
| 0.3 | 0.56 |
| 0.4 | 0.48 |
| 0.5 | 0.4 |
| 0.6 | 0.32 |
| 0.7 | 0.24 |
| 0.8 | 0.16 |
Sweep one variable
Variables and how each one contributes
Tractive efficiency
What the equation gives you. Everything else feeds it.
Ratio of drawbar pull to gross thrust
The ratio of the drawbar pull to the gross thrust: how much of the thrust is left after the motion resistance. It is less than 1. Directly proportional: if the resistance takes more of the thrust, the efficiency falls in step. Raising it by 10 % (to 0.88) moves the result by +10 %, from 0.64 to 0.704.
Driving slip
The driving slip, from 0 to 1. Lowers the efficiency through the factor (1 − s). A slip of 0.2 costs 20 % of the wheel power. Raising it by 0.1 (to 0.3) moves the result by −12.5 %, from 0.64 to 0.56.
Worked example with the values above
- Slip factor: 1 − s = 1 − 0.2 = 0.8.
- Multiply by the net-to-gross ratio: 0.8 × 0.8.
- ηtr = 0.64, so 64 % of the wheel power becomes drawbar power.
Assumptions and limits
- The simple factorisation H = Tw/Re and U = (1 − s) Re ω, which holds for simplified contact models.
- Steady travel on level ground, with the gross thrust and the motion resistance defined consistently.
Common mistakes
- Using the general definition and the factorised form with different torque or power references.
- Reporting the efficiency without the slip at which it was measured.
Statistics and uncertainty
The efficiency is a product of two measured ratios. DBP/H is a ratio of forces, each measured to 3 to 5 %, and s is derived from two speeds as shown above, with an error of ±0.02 or so. Soft soil adds scatter of ±10 % between passes, so a single tractive efficiency figure should always be given with the soil condition, the load and the slip.
Where it is used
- Comparing tyres and tracks on soil, and finding the working slip at which a vehicle is most efficient.
- Estimating fuel use or battery energy per unit of towed work.
Maths you need
- Efficiency: output power divided by input power
- Slip: fraction of wheel speed lost