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Piston engines reach full rpm within a second or two, but turbines take much longer. Why is that?

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    $\begingroup$ It's unclear from your question what you exactly mean. Do you mean the time to start up an engine, or to increase the RPM of an already running engine (e.g. from idle to full power)? $\endgroup$ – DeltaLima Jan 15 '14 at 13:30
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I'm not an engineer (which might be better suited to answer this) so this is from simplified things they feed pilots:

Jet engines take much longer to spool up (i.e. increase RPM) than piston engines, especially at low RPM because of the pressure ratio/increased airflow necessary to keep the compressor from stalling/surging/blowing up every time when changing power settings.

The (simplified) jet engine cycle contains a compressor that pushes air into a combustion chamber, where it burns, and then blows out the rear end rotating a turbine that moves the compressor from back where we started at.

If you "add more power" (i.e. put more fuel in) it takes a while for that extra fuel to produce more thrust, which in turn takes a while to accelerate the turbine, which will make the compressor spin faster, which will finally bring more compressed air into the combustion chamber to utilize all that extra fuel you poured in at step 1.

Adding power all of a sudden will increase the pressure in the combustion chamber, so much that air that is "upstream" (i.e still in the compressor) does not want to advance. The extra pressure in the combustion chamber did not have enough time to spool up the turbine, so now the compressor is underpowered to keep "pushing" compressed air into the combustion chamber. Air starts flowing backwards (i.e. from combustion chamber to compressor), engine surges, all hell breaks loose.

So there is a lag (electronically these days, the pilots can floor the trust levers as fast as they like) when the engines are at low RPM, the FADEC only adds a little bit of extra fuel, waits for the airflow to stabilize, then adds a little more, and so on.

I think the graph below might explain this. Every time you change RPM, you will increase Pressure Ratio (i.e. move up the graph), then you wait a little bit for Air Mass Flow to increase (i.e. move right). If you increase the Pressure Ratio too much, without the accompanying mass flow (which take a while because of inertia) you will enter the surge line.

enter image description here

A similar thing happens on spool down, albeit a gentler one.

Compare this with the piston engine where you put more air/gas mixture into the cylinder, it makes for a bigger bang, accelerates the piston faster, and the very next piston cycle you can theoretically get max power.

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    $\begingroup$ And turboprops take the middle ground. The turbine is always at 100% RPM and the prop changes pitch to keep it at 100%, in response to throttle input. Prop blade pitch changes very fast - less mass to move less distance; thrust comes on immediately. $\endgroup$ – radarbob Mar 27 '14 at 1:17
  • $\begingroup$ @radarbob: It's not that simple, because turboprops have propeller attached to the low pressure turbine and compressor to the high pressure turbine. So the high pressure turbine still has to spool up. Fortunately while the turbines are independent, keeping the low pressure one at high rpm via prop pitch changes the pressures so that the high pressure one keep high rpm too. And high pressure turbines generally always run at higher rpm anyway. $\endgroup$ – Jan Hudec Mar 28 '14 at 8:06
  • $\begingroup$ It should be noted that output power of piston engine is also limited by RPM, because one cycle can only intake so much air and thus burn so much fuel. Just the margin between throttled down and throttle fully open is much bigger. $\endgroup$ – Jan Hudec Mar 28 '14 at 8:10
  • $\begingroup$ @JanHudec, I may have under-qualified my comment; prop pitch change, and so thrust, was practically immediate in the aircraft I flew. The turbine ran @ 100% and the prop governed to maintain 100% rpm. If parts of the engine were different that certainly was not evident in any procedures, limitations, or gages. $\endgroup$ – radarbob Mar 30 '14 at 4:53
  • $\begingroup$ @radarbob: The turbine should mean the high pressure stage. I suppose the low resistance provided by the power turbine at high rpm but low power can keep the high pressure turbine running at 100% or almost so. $\endgroup$ – Jan Hudec Mar 30 '14 at 19:43
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Car guy here.

Fundamentally, it's due to turbine engines relying upon the compressor charge to push the exhaust from the combustion chamber through the turbine blades. Increasing pressure in the combustion chamber too rapidly can push back against the flow from the compressor side, which stalls the engine and probably can damage the compressor blades.

On a piston engine, power is made in (mostly) distinct strokes. Rapidly increasing the pressure during the power stroke will not push back against the intake charge since the intake valves for that cylinder will be closed at that time.

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  • $\begingroup$ And if the fuel/air charge is ignited too early in a piston cycle, it can destroy the engine! (See "knock".) $\endgroup$ – feetwet Apr 21 '18 at 16:16
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Momentum is given by:

$$\mathrm{Momentum}=\mathrm{Mass}\times\mathrm{Velocity}$$

Work done is given by:

$$\mathrm{Work~done}=\mathrm{Force}\times\mathrm{Distance}$$

Work done is measured in watts, defined as joules per second.

Knowing this, you can see how a battery will behave with a bigger load.

A jet engine has a larger mass, and must reach a higher velocity. The work done to do so will increase too, with a more powerful battery doing more rotations. The thing is, it's not a proportionally larger battery. If you gave jet planes a really powerful battery, the work done would be huge, and a lot of force would be applied in very little time (high wattage), so that it would start up in the same time as a prop. However, this would be very energy inefficient (due to heating), so it works out best to use a smaller battery to start up over a longer period of time.

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    $\begingroup$ Dan, I interpreted the question differently. Not how long it takes to start the engine from stopped, but how long it takes an idling engine to spool up. I do know that first generation jet engines had prolonged spool up times, and modern designs spool up much more quickly, but I don't know the physics of why. $\endgroup$ – Skip Miller Jan 14 '14 at 16:40
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    $\begingroup$ Ah, well the same thing can be applied. The change in angular momentum between two speeds will be much, much greater on a jet engine, for the same reason as above :) $\endgroup$ – Dan Jan 14 '14 at 16:50
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    $\begingroup$ Dan, I just found this from the headline of an article in a "JET POWER" blog. "Engine thrust is APPROXIMATELY proportional to the engine speed raised to the power of 3.5". If this is correct, it means that an idling jet engine has very little surplus power should the thrust lever be advanced fully, until the engine spools up. Coupled with your correct comments above about the rotating mass and angular momentum being larger than on a piston engine, it is clear that it will take longer for the jet to reach full power. $\endgroup$ – Skip Miller Jan 14 '14 at 17:07
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    $\begingroup$ In a turbine engine, things are very different. It's not safe to begin combustion until the compressors are already running at a relatively high RPM, such that the combustion is contained within the combustion chamber. A jet engine doesn't have a sealed-off combustion chamber like a piston engine. The combustion is contained by the high air pressure produced by the compressors. If that air pressure isn't present yet (which it isn't in an engine that isn't spinning,) the combustion would not be contained and would fire right out of the front of the engine. Needless to say, that's bad. $\endgroup$ – reirab Apr 10 '14 at 19:56
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    $\begingroup$ Oh, another issue regarding turbine engines: They don't typically use electric starters at all. They're started with external high-pressure air streams (either bleed air from an APU or an already-running engine or from a start cart.) See this question: How are turbine engines started?. $\endgroup$ – reirab Apr 10 '14 at 20:40

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