External forces offer rolling resistance to the motion of wheeled vehicles, such as tractors and scrapers. The engine has to supply power to overcome this resistance; the greater the resistance is, the more power needed to move a load. Rolling resistance depends on the weight on the wheels and the tire penetration into the ground:

R = R_f W + R_p PW

where
R = rolling resistance, lb (N)

R_f = rolling-resistance factor, lb/ton (N/tonne)

W = weight on wheels, ton (tonne)

R_p = tire-penetration factor, lb/ton in (N/tonne mm) penetration

p = tire penetration, in (mm)

R_f usually is taken as 40 lb/ton (or 2 percent lb/lb) (173 N/t) and R_p as 30 lb/ton in (1.5% lb/lb in) (3288 N/t mm).

Hence,the above equation can be written as

R = (2% + 1.5 % p ) W’ = R’ W’

where
W’ = weight on wheels, lb(N)
R’ = 2% + 1.5%p.

Additional power is required to overcome rolling resistance on a slope. Grade resistance also is proportional to weight:

G = R_g s W

where
G = grade resistance, lb(N)

R_g­ = grade-resistance factor = 20 lb/ton (86.3 N/t) = 1% lb/lb (N/N)

s = percent grade, positive for uphill motion. Negative for downhill

Thus, the total road resistance is the algebraic sum of the rolling and grade resistances, or the total pull, lb ( N ), required:

T = (R’ + R_g s ) W’ = (2% + 1.5%p + 1%s)W’

In addition, an allowance may have to be made for loss of power with altitude. If so, allow 3 percent pull loss for each 1000 ft (305 m) above 2500 ft (762 m).

Usable pull P depends on the weight W on the drivers:

P = f W

where
f = coefficient of traction.