# Drive: Design of hydraulic motors

## Drive calculation for vehicles

### 1. motor speed: n, RPM

v km – vehicle speed, km/h;

v ml – vehicle speed, mil/h;

Rm – rolling radius wheel, m;

Rin – rolling radius wheel, in;

i – transmission factor from motor to drive wheels. Without transmission gear, i=1.

### 2. rolling resistance: RR, daN [lbs]

Resistance force, which results from the contact of the wheels on different surfaces:

RR=G x ρ

G– total weight of the vehicle load, daN [lbs]

ρ– coefficient of rolling resistance (Table 1)

### 3. gradient resistance: GR, daN [lbs]

GR=G x (sinα + ρ x cosα)

α – inclination angle (Table 2)

### 4. acceleration force: FA, daN [lbs]

The force FA, required to achieve acceleration from 0 to a maximum velocity v in time t, is calculated using the following formula:

FA – acceleration force, daN [lbs]

t – time, [s].

### 5. tensile force: DP, daN [lbs]

Tractive force DP is the additional tractive force required to move the trailer. This value is calculated as follows:

• according to the designer’s assessment
• by calculating the forces according to points 2, 3 and 4 for the trailer; the calculated sum corresponds to the tractive force sought

### 6. total tensile force: TE, daN [lbs]

The total tractive force TE is the tractive force needed to move the vehicle; this is equal to the sum of the forces calculated according to points 2 to 5 with a   increase of 10% due to air resistance.

TE=1,1 x (RR + GR + FA + DP)

RR – force needed to overcome rolling resistance;

GR – force needed to overcome the slope;

FA – force needed for acceleration (acceleration force);

DP – additional traction effort (trailer).

### 7. torque of the motor: M, daNm [in-lb]

Required torque for each hydraulic motor:

N – number of motors;

ηm-mechanical efficiency of the gearbox (if any).

### 8. wheel adhesion: MW, daNm [in-lb]

To avoid wheel slip, MW should be larger than M.

f– Coefficient of friction;

GW– total weight over wheels, daN [lbs]