# What are the formulas for the expression of wheeled car power? 1. Resistance and dynamics of car operation
(1) Running resistance. The resistance of the car in operation is shown in Figure 1. These resistances are related to the total weight, shape, running speed, acceleration, gradient and road conditions of the car, and can be expressed as
R=Rr+N+Rac+Rn
where R is the running resistance;
Rr – rolling resistance;
N – air resistance;
Rac – acceleration resistance;
Rn – Ramp resistance.
The running resistance is mainly related to the speed and acceleration when the total weight of the car, its shape, slope, and road conditions are determined.

(2) Running power. The traction force (driving force) is in a balanced state when F=R; it accelerates when F>R.

(3) The work required for operation.
W=F·S
where W is the work required for operation;
F – running traction;
S—running distance.

(4) Power required for operation.
P=W/t=(F·S)/t=F/ν

where P is the power required for operation;
ν – speed.

2. Balance equation
The balance equation in car operation can be expressed as
P=(1/η)[Gfν+Giν+bmν(dν/dt)+CAν3]

where η——transfer efficiency;
G – self-weight + load of the car;
ν——car speed;
f——rolling friction coefficient;
i——slope;
b——acceleration coefficient;
m – the mass of the car;
C——air resistance coefficient;
A – Windward area.

The above formula is a theoretical formula, in which the four items in parentheses are the frictional resistance Rr, the ramp resistance Rn, the acceleration resistance Rac and the air resistance N, of which the rolling friction coefficient f and the air resistance coefficient C are related to the car type, see Table 1.

3. Influence of running speed on resistance
The effect of running speed on resistance is shown in Figure 2. It can be seen that after the car weight G, road condition f, gradient i, and C and A related to wind power and car type are set, the resistance is mainly related to the speed of the car. The effect of speed on the rolling resistance coefficient of different tire pressures and the effect of speed on the air resistance and rolling resistance coefficient are shown in Figure 2(a). , the smaller the friction coefficient; and, the faster the car speed, the greater the proportion of air resistance.

4. Influence of tire type and road surface on braking and driving force
During braking and driving, the tangential force generated by the friction between the tire and the road surface will generate a certain slip, and its value is expressed by the slip rate s:
When v>Rω(braking), s=(ν-Rω)/v
When v<Rω(drive), s=(ν-Rω)/Rω
where ν——car speed;
ω – wheel rolling angular velocity.
When locked, s=1, when not slipping, s=0. As shown in Fig. 2(b), when s is around 0.1~0.3, the braking force is the largest.

5. Examples of Dynamic Calculation Methods for Wheeled cars
(1) Wheeled car resistance: R=Rr+N+Rac+Rn
Rr=fWcosθ
where θ——slope angle;
f——Friction coefficient, car 0.018, bicycle 0.005~0.01, solar car 0.0035;
N=ρCdAν²
where ρ——0.04728kg/m³;
Cd——drag coefficient;
A——Area, m²;
ν——speed, km/h;
Rac=(W+Wr
where W——total weight, kg;
Wr——the equivalent weight of the rotating part, kg;
a——acceleration, m/s²;
Rn=W sinθ
(2) Required power:
P=Rs/t
= Rν
=(Rr+N+Rac+Rn