Calculating torque

[Nick Sumner]

Is it possible to calculate the torque of an engine if only the piston volume, RPM and the type of fuel are known?

If accurate calculation is impossible is an estimate possible?

[gruad]

Torque is force times distance and in the case of an engine would be the force exerted by the piston at the varying distance of the crank from the bearing. Gears can increase torque at the expense of rpm.

I would suggest that the above principle could be made into an approximate formula. Certainly the more offset the crank is the more torque, and the longer the stroke would be required.

I reckon if you did some hunting you could find the formula.

[Red Admiral]

Power = torque x angular velocity

You'll most likely have a power figure for most engines. The angular velocity is calculated from the rpm = 2 * pi / 60

[Nick Sumner]

Can the force exerted by internal combustion in one of the cylinders of a four stroke engine be calculated from piston speed?

[Wuzak]

quote:Originally posted by Nick Sumner

Can the force exerted by internal combustion in one of the cylinders of a four stroke engine be calculated from piston speed?




No, I doubt it. You would need to know all the geometry of the engine (bore, stroke, rod length), and the pressure in the cylinder during the expansion of the burning gases.

[Nick Sumner]

If you know the fuel type is the pressure in the cylinder during the expansion of the burning gases a constant?

[Red Admiral]

quote: If you know the fuel type is the pressure in the cylinder during the expansion of the burning gases a constant?

http://www.grc.nasa.gov/WWW/K-12/airplane/Images/otto.gif

No. The Otto-cycle engine (petrol) has combustion at a constant volume. The diesel cycle has combustion at a constant pressure

[Nick Sumner]

Sigh…

OK, I’m going to let rip with one of my fearless displays of ignorance. [:I]

I’m interested in calculating the theoretical power that might be obtained from a 75 Litre H 24 engine such as the one Napier were designing at the close of WW2. It is for a piece of fiction.

I have not been able to pin down much information on it except the configuration and total swept volume.

I am assuming a cylinder size of 6.5 by 5.75 inches which corresponds to 4584 cubic inches or 75 litres.

I am assuming a reasonable piston speed (ie 16 meters per second which equates to 3148 feet / minute though of course the sabre's piston speed was slightly higher. The Centaurus, which is of a similar vintage but different configuration (including a narrower bore and a longer stroke 5.75 X 7 inches) had a piston speed of 3260 f/m.)

This gives us about 3300 RPM, well below the Sabre VII’s maximum of 3850 – 4000 RPM

So using the formula

Angular velocity = 2rpm X pi / 60 (which I think is what Red Admiral meant – if not forgive me I am mathematically challenged)

Then I make the angular velocity to be 345.4

But that only gets me so far as the only formulas I’ve been able to find on the internet to calculate HP are;

HP = RPM X torque/ 5252

HP = MEP X displacement X RPM / 792

And the only formulas I’ve been able to find on the internet to calculate torque are

Torque = 5252 X HP /RPM

Torque = MEP X displacement

And Red Admiral’s

Power (I assume in Watts) = torque x angular velocity

It seems I need either a figure for torque or one for MEP – anyone got a guess?

[Wuzak]

If you have a BMEP (MEP) number and engine size we can work out the power, then we can work back to get torque...

Taking the Sabre for reference with 2850 at 3800rpm.

From that we calculate a BMEP of 1830kPa.

Now, using your defined bore and stroke and the 16m/s average piston speed we can calculate that the engin will run at 3287rpm. Using the BMEP forumla we find that the power developed is 3762kW (5043hp).

To calculate torque, we find the angular velocity and divide the power by it. Angular velocity is 344 radians per second, and torque therefore is 10.9kNm (10900Nm).

Sorry I haven't enough time to go through this completely for you.

[Nick Sumner]

quote:Originally posted by Wuzak


Sorry I haven't enough time to go through this completely for you.


Please don't apologise, I really appreciate you taking the time to do this and if you went in to a lot of detail there is a fair chance I wouldn't understand it!

Thank you very much!

[Red Admiral]

Tha graph I posted before is a standard p-v diagram which can be drawn for any 4-stroke petrol engine by taking measurements of pressure. You can work out the volume by the geometry of the engine. The area enclosed on the graph is the Mean Effective Pressure (MEP). This can be used to make comparisons between engines without taking into account their displacement, sort of like a Lift Coefficient for aircraft. It is possible to do this because the graph deals with volume change and not volume as a total. MEP isn't particularly useful as there are losses in the engine. This is why Brake Mean Effective Pressure (BMEP) is used instead where the available power is measured at the output shaft using a friction brake.

BMEP = 960 * Power / rpm * displacement (for BMEP in bar, also used psi)

NB. 1 Bar is 100,000Pascals and is more or less atmospheric pressure.

Less BMEP will generally mean less stress on the engine and more reliability (or less weight) but less power.

With a BMEP of 15 and rpm of 3000 we get a power of 3500hp. This would be for a bomber engine rather than a fighter engine. If we reduce the rpm to 3000 then sleeve valves don't really need to be used. However as this is from Napier we'll assume sleeve valves and raise the rpm close the maximum 3300rpm (because of limits on piston ring wear). Use a much higher boost from 145/150octane fuel to raise the BMEP to around 25bar. Power goes up to 6450hp! and that BMEP figure is still not near the maximum used for that special Merlin engine. You'll be wanting a massive contra-prop to deal with that power. Maybe 8-blades and about 14ft diameter.

Ask if you have any questions.

[Nick Sumner]

Thanks Red Admiral!

quote:Originally posted by Red Admiral

You'll be wanting a massive contra-prop to deal with that power. Maybe 8-blades and about 14ft diameter.


Intriguingly that is an almost exact description of the Hawker P1030 projects propeller, though it was schemed for a 4000 HP engine.

[gruad]

Messing around with formulae:

If we have b = bore, s = stroke

If the piston's area is A and the pressure of the gas above atmospheric is P then the force exerted will be

F=P*pi*r^2 = P*pi*b^2/4

If we assume maximum torque is generated where the crank is furthest away from the centre line of the piston ie mid stroke then the torque will be.

T=F*s/2 (since the crank action is half the stroke)

Putting this together gives

T=P*pi*b^2/4 * s/2.

But we know the volume of the cylinder V = pi*b^2/4 * s

So T=P V/2

However we have to remember that this is a 4 cycle engine and the torque is only available on the combustion stroke and infact there is negative torque exerted by the other 3 cycles.

If we take a guess and assume that during the combustion stroke the average torque is half that of the maximum then the average torque over the whole cycle will be 1/8 of the maximum

So I get the rough formula

T = V*P/8

I think though the upshot from this is that Torque varies in proportion with cylinder size.

Thus a 75 Litre engine would produce approximately 3 times the torque of a 27 Litre engine.

This is me remembering my high school maths and physics so probably I have made a mistake somewhere!