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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 !

Ben Jo
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  • Many Q&A on here around this topic, this is but one : https://engineering.stackexchange.com/q/3321/10902 – Solar Mike Dec 05 '18 at 05:53
  • 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. – Carl Witthoft Dec 05 '18 at 16:29

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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.

kamran
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  • What about all the rotational inertia in the drivetrain ? shafts, gears etc... – Solar Mike Dec 05 '18 at 06:59
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    @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. – kamran Dec 05 '18 at 07:22
  • 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... – Solar Mike Dec 05 '18 at 08:04
  • @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. – kamran Dec 05 '18 at 08:21
  • My point is that it is not only the wheel but the axle shaft, differential, gears and it should be included... – Solar Mike Dec 05 '18 at 08:28
  • @SolarMike since braking should disengage the transmission -- or in a standard transmission ICE vehicle the engine itself dissipates energy as the RPM drops -- you're really only left with the axles and wheels, and the difference between their linear energy and rotational energy as viewed by an outside frame of reference is pretty small. – Carl Witthoft Dec 05 '18 at 16:29
  • @CarlWitthoft which manual transmission cars disconnect the transmission on braking? Sounds like a good idea but not seen one... Oh and for an emergency stop we were taught to only dump the clutch just before the engine stalled... Engine braking can be useful as well, which can reduce braking force from the friction devices... – Solar Mike Dec 05 '18 at 17:16
  • @kamran I take it you avoid clouds then... – Solar Mike Dec 05 '18 at 17:19
  • @SolarMike sorry -- I was referring to slush drives there. Yes, leaving the gearbox engaged leads to engine braking. – Carl Witthoft Dec 05 '18 at 18:30
  • @SolarMike, I have a Cessna 172, not a very well equipped with the latest navigation instrument for IFR. so I try to stay away from clouds. But CB and convective weather can surprise you with clouds forming right around you, before your eyes. – kamran Dec 05 '18 at 18:39
  • @kamran so you've read the "178 seconds" article then... – Solar Mike Dec 05 '18 at 18:44
  • @SolarMike, no! what's that? – kamran Dec 05 '18 at 18:46
  • @kamran want you to stay around so : https://www.flightsafetyaustralia.com/2016/01/178-seconds-to-live-vfr-into-imc/ – Solar Mike Dec 05 '18 at 18:48
  • @SolarMike, Yes, even watching the video made me shudder. the greatest joyful moments of your life turns fast into a death trap. It happened to me 4 years ago and the funny thing is because I was chasing the wales in the Pacific ocean near Catalina Island, i was recording the scene on my phone. I went into the haze and dove like a rock. Saw the clear skies only at 800 feet above waters. I did pull back just slightly as I had practiced many times, am still here though. It's an honorable deprture. – kamran Dec 05 '18 at 19:43