# Calculating the Braking Energy of a vehicle

you might find my question stupid. I am unfortunately not an engineer and didn't find the answer on google. I want to calculate the braking energy of a vehicle decelerating from v2 to v1 (km/h). Given are the Wheel inertia mass moment "I" and the wheel diameter "d" as well as the vehicle mass "M".

Could you give me the equation needed for that?

Thank you !

• Many Q&A on here around this topic, this is but one : engineering.stackexchange.com/q/3321/10902 Dec 5, 2018 at 5:53
• If this is homework, you're probably going to be expected to get the exact answer, so you will want to use the wheel term provided in the answer. Dec 5, 2018 at 16:29

there are two kinetic types of energy that are involved in a moving car:

Linear and rotational kinetic energy, $$K_{e \ linear} = \frac {1}{2}mv^2 \ ; K_{e \ rotatinal} = \frac {1}{2}I \omega^2$$

The deceleration from V1 to V2 will reduce the energy. This energy is being saved in hybrid and electrical cars as regenerative energy.

The linear energy change is equal to:

$$K_{e \ linear \ chang} = \frac {1}{2}mv_{1}^2 - \frac {1}{2}mv_{2}^2$$

And rotational energy change is equal to:

$$K_{e \ rotatinal \ change} = \frac {1}{2}I_{1} \omega^2 - \frac {1}{2}I_{2} \omega^2$$

And $$\ V = r \omega = d \omega/2 \ and\ \omega= V/r$$ with r being the radius of the wheel, r = d/2.

However, because of small "I" of the wheels compared to the mass of the car, the contribution of the wheel's change of energy is not significant.

• What about all the rotational inertia in the drivetrain ? shafts, gears etc... Dec 5, 2018 at 6:59
• @SolarMike, in most car engines the internal moving parts' energy is not aligned with the velocity of the car neither additive. The flywheel which is there to regulate a chaotic ensemble of non aligned trajectory of moving parts, doesn't closely follow the velocity of the car. RPM of the engine is regulated by a computer, in modern cars, which coordinates power demand, gearshifts, air density and temps, moisture, engine vacuum breathing, etc. Dec 5, 2018 at 7:22
• you obviously have not seen, or felt, the inertial impact of rotatrional machinery - especially notable when one dumps the clutch when trying to stop a tractor with a straw chopper is going full belt... That inertia can be considerable and will need to be dissipated... Dec 5, 2018 at 8:04
• @Solar Mike, I try to keep it focused and short. However I am a private pilot, and have to deal with changes in angular momentum of my airplane's engine. I will crash, if I don't apply corrective controls to compensate yaw, or roll. Dec 5, 2018 at 8:21
• My point is that it is not only the wheel but the axle shaft, differential, gears and it should be included... Dec 5, 2018 at 8:28