How to Calculate Vehicle Speed

Car transmissions can look complicated, and the actual working can seem to be even more complicated. A conventional constant mesh gear box consists of an input shaft from the engine, a counter shaft and a main shaft which delivers power to the differential via propeller shaft. To know more in detail about the working of a constant mesh gearbox, please visit the page on the following link: 

• How manual transmission works

As you can see in the diagram, a 4-speed constant mesh gearbox consists of a set of 11 gears (including the gears between the input shaft and the counter shaft). Now let’s calculate the gear ratio between the gears and how a gear ratio can affect the final drive given to the wheels? How to calculate the speed of the vehicle?

1^st gear:

Let’s say the gear A (driving) has 10 teeth and gear B (driven) has 35 teeth. Gear ratio is the ratio of number of teeth in the driven gear to the number of teeth in the driving gear.

Gear ratio = number of teeth in the driven gear / number of teeth in the driving gear

Therefore, 1^st gear ratio can be calculated as

G1 = T_B / T_A

G1 = 35/10 = 3.5 : 1

T_B = Number of teeth in gear B

T_A = Number of teeth in gear A

The differential has its own gear ratio which is known as the Differential gear ratio (G_D). In this case, let’s assume that G_D = 3.5. Now the G_D is fixed and cannot be altered.

Now to calculate the speed at which the wheels are rotating, we need to bring into picture the final gear ratio. Final gear ratio decides at what speed the wheels are driven. It is a product of both transmission gear ratio and the differential gear ratio together.

Final Gear Ratio (G_F) = G1 X G_D

G_F = 3.5 X 3.5 = 12.25

Yes, I know it is very complicated and you are lost somewhere in understanding the whole concept. To explain you in simple words, the final value of G_F = 12.25 indicates that for 12.25 revolutions of the engine crankshaft, the wheels will revolute only once.

Consider your engine running at 2000 rpm, then wheels will rotate at (2000/12.25) rpm.

To calculate the speed of the vehicle:

Let’s consider the tire is 0.35 m in diameter, therefore the circumference of the tire is 

C = πD

C = π(0.35)

C = 1.1 m (approx.)

Hence, for every 12.25 revolutions of the crankshaft, the wheels will cover 1.1 m.

Now let’s consider the engine speed in revolution per hour (rph) = 2000 x 60 = 1,20,000 rph.      

Now the vehicle speed can be calculated using the above values. The vehicle speed at 1^st gear at an engine speed of 1,20,000 rph is

Vehicle speed = (Engine speed in rph / final gear ratio) X circumference of the tire

Vehicle Speed = (1,20,000 rph / 12.25) X 1.1 m

= 10,775 meters per hour (approx.)

= 10.775 km/h

The vehicle speed for the other gear ratios can be calculated by following the same procedure as above. Let’s calculate:

2^nd Gear:

Let’s assume the 2^nd gear ratio, G2 = 2.5 : 1.

Differential gear ratio (G_D) = 3.5 : 1

Final gear ratio = 2.5 X 3.5 = 8.75 : 1

Engine speed = 200000 rph          

Vehicle speed at 2^nd gear = (200000/8.75) X 1.1

 = 25142.85 m/h 

= 25 km/h (approx.)

3^rd gear:

Let’s assume the 3^rd gear ratio, G2 = 1.8 : 1.

Differential gear ratio (G_D) = 3.5 : 1

Final gear ratio = 1.8 X 3.5 = 6.3 : 1

Engine speed = 200000 rph          

Vehicle speed at 3^rd gear = (200000/6.3) X 1.1 

= 34920.63 m/h 

= 35 km/h (approx.)

4th Gear:

Let’s assume the 4^th gear ratio, G2 = 1 : 1.

Differential gear ratio (G_D) = 3.5 : 1

Final gear ratio = 1 X 3.5 = 3.5 : 1

Engine speed = 200000 rph          

Vehicle speed at 4^th gear = (200000/3.5) X 1.1 

= 62857.14 m/h 

= 63 km/h (approx.)