# How to find the Force of a Car's exhaust?

## Main Question or Discussion Point

Hey guys! I'm brand new to the forum and looking for some advice. For full disclosure, I am actually an Economics major, but I absolutely love learning about mechanical engineering; more specifically automotive mechanical engineering. Haha. I have been looking all over the web for about a month now but have yet to find an answer to my question, which is this:

How do I calculate the amount of force a car engine's exhaust produces after leaving the cylinders?

The eventual idea is to capture the force by way of a turbine. I think of it kind of like a watermill and a stream. I am talking about right as it leaves the cylinders (think of where the turbine of a turbocharger would be). I realize the amount of Force would depend on things like rpm's, air density, psi, engine displacement, volume of the turbine, etc. resulting in a range of values.

So how would y'all figure it out? Any and all help is GREATLY appreciated!

## Answers and Replies

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You could make it pretty simple. Use the combustion formula to calculate the resultant pressure due to the conditions inside the motor, and the force exerted by it as it leaves the exhaust would just be due to the pressure difference and the size of the exhaust.

Personally, I'm lazy and would just calculate the localised conditions as a result of the combustion and run a CFD simulation with a simplified 2D mesh. I think the hardest part would be to get accurate data for the information required. Treating it as thrust would also be interesting.

Bobbywhy
Gold Member
fshzyby, Welcome to Physics Forums!

I don't know how to answer your question, but will offer an observation for you to consider. When we were teenagers we found we could cause a car's engine to stall out and stop by simply putting our shoe flat against the exhaust pipe exit, effectively closing it. I guess the "back pressure" was felt at the exhaust valve openings, causing the engine to stall. So, your proposal to harvest power from this system using a turbine seems to not be viable.

But do not be discouraged: harvesting heat energy from internal combustion engines is already being done! See:

“Harvesting Energy with Nanotechnology
With 58% of the energy generated in the United States wasted as heat, researchers at Purdue University are working on a technique that uses nanotechnology to harvest energy from hot pipes or engine components to potentially recover energy wasted in factories, power plants and cars. http://chipdesignmag.com/lpd/blog/tag/harvesting-energy/

This paper will address how heat emitted by exhaust systems can be captured and used to increase vehicle efficiency:
http://saematman.saejournals.org/content/4/1/1211.abstract

An automotive thermoelectric generator (ATEG) is a device that converts waste heat in an internal combustion engine (IC) into electricity using the Seebeck Effect.
http://en.wikipedia.org/wiki/Automotive_thermoelectric_generator

Cheers,
Bobbywhy

Thank you both. Vadar, I'll check out your suggestions. Bobby, I am operating under the assumption that the amount of back pressure due to the added turbine wouldn't stall the car. That is the case with turbochargers anyway, though that could be because the added power is enough to overcome any adverse effects, if that makes any sense.

Bobbywhy
Gold Member
I always thought turbochargers were applied to the "intake" side of the engine, and not the "exhaust" side.

A turbocharger is made up of a compressor and a turbine. The compressor (which is on the intake side) is driven by the turbine (on the exhaust side). The turbine is powered by the exhaust of a car. And just for fun, the difference between a supercharger and turbocharger is that a supercharger's compression is driven by a belt from the engine it's self, so while the engine loses hp, turning the supercharger, but because of the compressor, there is a net power gain :)

The engine is stalling because you are changing the conditions at wich combustion occurs. In this case it will eventually become an environment where it cannot occur. I'll spare you a chemistry lesson.

Bobbywhy
Gold Member
Thank you for the clarification. I confused "turbo-" with "super-". So whenever you install a turbine (to do some work) in the exhaust system it will absorb (take from) the hp output of the engine? Is this your plan in the opening post?

Cheers,
Bobbywhy

jack action
Science Advisor
Gold Member
The eventual idea is to capture the force by way of a turbine. I think of it kind of like a watermill and a stream. I am talking about right as it leaves the cylinders (think of where the turbine of a turbocharger would be).
I don't understand, you are exactly describing what the turbine of a turbocharger does. The way it works is not by determining the amount pressure you can put in front of the turbine, but by knowing the capabilities of your turbine. For example, here's a typical turbine map:

There are actually 5 different turbine models on this map. For a given mass flow rate, there is a corresponding pressure ratio across the turbine. Since we all know that at the turbine exit the pressure is 14.7 psi (atmospheric pressure), then a pressure ratio of 2 means that the inlet pressure must be 29.4 psi. As you can see, for every turbine design, once you reach a certain inlet pressure, the flow is choked and increasing the pressure has no more effect on flow rate (so it only blocks the outlet of your engine cylinders).

So it is not really about how much pressure you can generate to push a turbine, but how much energy a turbine can recover from a given mass flow rate. The pressure will «adapt» itself to the conditions. You can then design the valve event of your camshaft for the proper exhaust gas conditions (pressure and flow rate).

The subject is even slightly more technical and this site has a nice intro about the subject.