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Terramechanics and off-road mobility

Drawbar pull

The net pulling force a vehicle has left for towing or accelerating on level ground: the gross tractive thrust minus all resistances from the terrain and the vehicle running losses.

Ref
TER-01
Rev
v1
Field
Terramechanics and off-road mobility
Result
DBP [kN]

H is the gross tractive thrust: the total forward force the wheels or tracks develop against the ground. Rmotion is everything that resists motion on level ground: soil compaction, bulldozing, rolling resistance, internal friction and air drag. DBP is what is left for towing or accelerating. Grade and the towed load are separate terms in the full balance, H − Rmotion − m g sin θ − Ftow = m U̇. Count each loss once: if soil compaction is already inside H (a net thrust), do not subtract it again in Rmotion.

The net pulling force a vehicle has left for towing or accelerating on level ground: the gross tractive thrust minus all resistances from the terrain and the vehicle running losses.

Calculator

Solve for
kN
kN
10150
kN
2100
  • Ratio of net to gross thrust, DBP / H0.625
  • Share of the thrust lost to motion resistance37.5 %
  • Motion resistance as a multiple of the drawbar pull, Rmotion / DBP0.6

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.

Drawbar pull (kN) current value 25 kN
HGross tractive thrustKey driver
−5135
RmotionTotal motion resistance
−6038
  • With 40 kN of thrust and 15 kN of resistance, 62.5 % of the thrust is left as drawbar pull (25 kN). If the ground softens and the resistance doubles to 30 kN, the pull falls to 10 kN, a loss of 60 %.
  • This is why vehicles get stuck in soft ground without losing any engine power: the resistance takes more and more of the thrust until nothing is left for the pull.
Chart data as tables

Ranked variables

VariableTypical rangeLowest resultHighest resultSwing (kN)Local stepChange in result
H Gross tractive thrust10 to 150 kN−5135140+10%+16 %
Rmotion Total motion resistance2 to 100 kN−603898+10%−6 %

Sweep of Total motion resistance

Total motion resistance (kN)Drawbar pull (kN)
238
14.2525.75
26.513.5
38.751.25
51−11
63.25−23.25
75.5−35.5
87.75−47.75
100−60

Sweep one variable

Drawbar pull (kN)Hover, touch, or use the arrow keys on the chart
−60−40−2002040 20406080100 Total motion resistance (kN) now 25

Variables and how each one contributes

DBP

Drawbar pull

Result · kN

What the equation gives you. Everything else feeds it.

H

Gross tractive thrust

kN · typical 10 to 150

The gross tractive thrust developed by the running gear against the ground, in kN. Adds directly. Because the resistance is subtracted, the drawbar pull changes by a larger percentage than the thrust itself. Raising it by 10 % (to 44) moves the result by +16 %, from 25 to 29 kN.

Rmotion

Total motion resistance

kN · typical 2 to 100

The total motion resistance on level ground, in kN, from soil compaction, bulldozing, rolling and internal friction. Subtracts directly. On soft ground this term grows quickly, which is what limits the pull. Raising it by 10 % (to 16.5) moves the result by −6 %, from 25 to 23.5 kN.

Worked example with the values above

  1. Gross thrust: H = 40 kN. Motion resistance: Rmotion = 15 kN.
  2. Subtract: DBP = H − Rmotion = 40 − 15.
  3. DBP = 25 kN, which is 62.5 % of the gross thrust.

Assumptions and limits

  • Steady level-ground travel, with the thrust and the resistance measured over the same conditions of slip and sinkage.
  • The resistances are counted once and in the same place as the thrust definition (gross or net) used.

Common mistakes

  • Subtracting the soil compaction twice, once in the resistance and once in a net thrust.
  • Using the engine force at the tyre as H on soft ground. The soil, not the engine, limits the thrust.

Statistics and uncertainty

DBP is a difference of two uncertain numbers, so its relative error is larger than either. With H = 40 ± 4 kN and Rmotion = 15 ± 4.5 kN (soil resistance is rarely known better than ±30 %) the pull is 25 ± 6 kN, an error of about 24 %. Measured drawbar pull from towing tests is far more reliable than a calculated value on soft ground.

Where it is used

  • Towing, recovery and winch assessments for off-road vehicles.
  • Comparing tyres and tracks by the pull they deliver on a given soil.

Maths you need

  • Forces in equilibrium: net force = thrust − resistance
  • Units: kN and N

Related formulas

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