Performance  
       
     
  Lateral Acceleration   Longitudinal Acceleration  
     
     
  Braking   Accelerating  
       
                                      
Power Limited   Traction Limited   Speed, Distance & Time   Hill Climbing   Axle Load Distribution

acceleration forces

From the previous figure (and assuming four identical tires), we can define the total force from the tires (Ft), the total rolling resistance (Fr) and the net vertical force (Fv):

Ft = Ftf + Ftr
Fr = Frf + Frr = frFv
Fv = mg − FLf − FLr = mg − FL = ( 1 − 
FL
mg
 ) mg = ( 1 − 
0.5ρCLAv2
mg
 ) mg

When accelerating, the power can be transmitted to the road with the front axle (FWD), the rear axle (RWD) or both (AWD) depending on the automobile layout.

Also, if we sum up the forces in the horizontal direction:

λmma + FD = Ft − Fr (1a)

To take into account the inertia due to the rotating parts, ma is multiplied by the mass factor (λm). This site assumes an average mass factor of 1.07 for a direct drive. For a typical road vehicle, it assumes a 6-speed transmission shifting every 1/6th of the top speed with the following mass factors for each gear ratio (from first to last): 1.19, 1.12, 1.08, 1.07, 1.06 and 1.05. This will also work with most older vehicles with 3- or 4-speed transmission as well, as such vehicles are usually not set up to reach their potential top speed.

From equation (1a) we get:(more)

a =
1
λm
 [
Ft
m
 − frg −
0.5ρ
m
 ( CDA − frCLA ) v2 ]
(1b)

This defines the acceleration of the vehicle at any speed v. To identify the maximum possible acceleration, we need to know the maximum tractive force, either based on power or traction availability.

Also, the maximum speed (vmax) that can reach a vehicle will happen when its acceleration will be zero (i.e. no more speed gain).