# Wankel/rotary engine efficiency

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1. Aug 26, 2016

### williamcarter

I was just wondering how we can find out the efficiency of a rotary engine?

Obvious, it is more efficient than a gasoline/diesel engine.For example the RX8 on 1.3 L in 2 rotors get 250 hp which is quite impressive for that capacity,also it works in 4 stroke,and the power to weight ratio is good.The only disadvantage would be the pollution that occurs, due to emmisions.

From my knowledge the diesel is more efficient than a gasoline due it's bigger compression ratio , hence more torque at lower revs.This can be proven thermodinamically using the efficiency formulas that imply compression ratio.

I am curious what types of calculations would be required to find out the efficiency of such engine , because I would like to plot a Power output(HP) vs Tq(torque) diagram,on different revs.

Last edited: Aug 26, 2016
2. Aug 27, 2016

### Nidum

3. Aug 27, 2016

### williamcarter

Thank you sir !

4. Aug 27, 2016

### SteamKing

Staff Emeritus
The same as any other heat engine. Measure the amount of energy (or work) produced in a given amount of time and the theoretical amount of heat which can be furnished from the quantity of fuel used. The resulting efficiency can then be determined by a simple calculation.
Maybe. Some impressive strides have been made recently with electronic engine controls which allow conventional engines to boost power output while not adversely affecting fuel economy. This suggests that an overall improvement of thermodynamic efficiency for these engines has occurred.

The tiny Ford EcoBoost 3-cylinder 1 liter engine is turbocharged and can produce as much as 138 HP in certain versions, yet the engine itself weighs less than 100 kg or so.

https://en.wikipedia.org/wiki/Ford_EcoBoost_engine
The same type of calculations can be done to analyze a Wankel engine as to analyze a piston engine. Both types of engine use the Otto cycle, but it is a tad more difficult to calculate the compression ratio of a Wankel engine, given the complex geometry of the rotor.

I'm not sure what plotting torque and power will do for you.

In metric units:

$Power = \frac{2\pi ⋅ Torque ⋅ RPM}{60}$

Power is in watts and torque is measured in newton-meters. RPM of course is engine speed in revolutions per minute.

5. Aug 27, 2016

### Staff: Mentor

Is it really the compression ratio that is responsible for higher efficiency, or is it higher temperature of the combustion products? (Not that these are completely unrelated, but one is a cause and the other is the effect).

6. Aug 27, 2016

### SteamKing

Staff Emeritus
Well, a lot of the thermo theory for the Otto cycle uses the compression ratio to calculate the state points of the cycle. The CR is a geometric property of the actual machine and is easy to calculate/determine. You could use gas temperatures and pressures at key points in the cycle to describe it, but this data is much more difficult to come by without taking some sophisticated measurements.

7. Aug 27, 2016

### jack action

Be careful when you compare the displacement of a Wankel engine to a typical 4-stroke engine. The first one represents the displacement per revolution and the second one is the displacement per cycle (which is 2 revolutions). In this case, there is a factor of 2 between the two. More info on this page (click (more) next to Displacement and Comparing Wankel and piston engines).

8. Aug 27, 2016

### billy_joule

The rotary is actually very inefficient (as anyone who's owned one will tell you, they are thirsty!).

some comparisons to regular 4 stroke petrol cars:
A golf GTI has similar power & weight as the RX8 but has 55% better fuel economy.
A Corvette has similar economy as the RX8 but almost twice as much power.

The long story:

While comparing peak power to economy isn't a perfect proxy for efficiency I think it'd still be representative.