Engine and Propeller Efficiency
Text Contents ] Chapter Contents ] Overview ] Definitions of Terms ] Fuel Flow vs Velocity Graphs ] L/D Ratio and Glide Performance ] Specific Fuel Consumption ] Jet Aircraft Range and Endurance ] Cruise Control ] Propeller Aircraft Range and Endurance ] [ Engine and Propeller Efficiency ] Range and Endurance Summary ] Climb Performance ]

 

So far we have said that for the jet engine fuel flow is proportional to thrust produced. For the propeller engine fuel flow is proportional to power produced. This has lead to the following conclusions about range and endurance.

Our conclusions were based on our earlier assumption that:

        TSFC is constant for a jet

        SFC is constant for a piston or turbo-prop

If the above is true then:

Jet

1. Max SE does not change with altitude.

2. Max SR improves with altitude.

Prop

1. Max SE decreases with altitude.

2. Max SR does not change with altitude.

Our assumptions were only approximations however. We must now consider the factors which change the TSFC and SFC.

Jet Engine Efficiency

Jet engines are designed to turn at much higher rpm than piston engines. They are also quite sensitive to changes in rpm. In other words, they loose efficiency if throttled back to low rpm. Jet engines also convert fuel more efficiently in low outside air temperatures. We can summarize by saying jet engines are:

  1. More efficient at colder air temperatures

2.      More efficient at high rpm

It is also worth noting that jet engine efficiency is NOT affected by velocity (in subsonic flight) or air density.

A graph showing maximum thrust produced by a jet engine will look like the one shown to the right.

The available thrust does not change with velocity. However, it does decrease with altitude.

We will return to this when we look at climb performance on the next page.

Thrust declines with altitude

 

Given that power equals thrust times velocity (P=TxV/325) a graph of THP available for a jet engine will look as shown to the right.

You can easily see why it is more appropriate to specify the “size” of a jet engine by quoting its sea level thrust rating, rather than the horsepower.

Power available - Jet

Turbo-prop Engine Efficiency

Turbo-prop engines are actually just jet engines with gear boxes and propellers attached. Therefore, the same factors affecting the efficiency of the jet engine described above also apply: In other words turbo-prop engines are:

1.      More efficient at colder air temperatures

2.      More efficient at high rpm.

The BHP and SHP output of the turbo-prop engine does not change with Velocity.

However, power does drop with altitude.

Below we will consider propeller efficiency. You will see that THP is NOT constant with velocity.

 Piston Engine Efficiency

Piston engines are remarkably consistent in their efficiency, compared to turbine engines. In other words efficiency does not change much with air temperature or rpm.

The only significant factor affecting the efficiency of the piston engine is throttle setting. When the throttle is retarded (making the manifold pressure lower than surrounding air pressure) the engine looses efficiency.

Pilots should keep in mind that a given amount of power can be produced by an infinite number of manifold pressure (MP) and rpm combinations. For example the following  MP x rpm combinations all produce equal amounts of power:

        22 x 2400

        23 x 2300

        24 x 2200

The engine will be more efficient if the pilot choose the higher MP and lower rpm combination (i.e. The third choice above.)

It is critical to note that none of the above theory will do any good at all unless the pilot leans the mixture to the maximum economy setting, as specified in the Pilot Operating Handbook.

Turbo-chargers allow a piston aircraft to fly faster and higher. However, the turbo-charger also tends to make the engine run hot, because it heats the air as it compresses it. Therefore, above some critical altitude the engine will overheat unless the mixture is richened to help cool it. As soon as this is happens the overall efficiency of the engine begins to decline.

Based on all the above, any power setting will have an optimum altitude(s) for the piston engine. These will be the altitude(s) at which full throttle produces the desired amount of power, with the mixture set for maximum economy.

Just as with the Turbo-prop engine discussed above, the BHP of the piston engine is independent of velocity.

In a normally aspirated piston engine BHP decreases with altitude. A turbocharger will maintain the power with altitude until the critical altitude is reached. Then power will decrease with altitude.

Propeller Efficiency

In addition to the engine efficiency factors described above the piston and turbo-prop aircraft must also contend with the efficiency of the propeller at converting the power into thrust. The following discussion about propeller efficiency applies equally to piston and turbo-prop aircraft.

Propeller efficiency refers to the percentage of Brake Horsepower (BHP) which gets converted into useful Thrust Horsepower (THP) by the propeller. The propeller is never 100% efficient. Therefore the propeller efficiency is always a number less than one. The definition is:

Neta is propeller efficiency.

In the last chapter we saw that the efficiency of a wing (as measured by the maximum L/D ratio) depends upon the aspect ratio of the wing and the angle of attack at which the wing operates. The efficiency of a propeller depends upon the same things. In other words propellers with high aspect ratios will be more efficient than short stubby propellers. Additionally, each propeller will have an optimum angle of attack. When operated at the optimum angle of attack the propeller will be most efficient.

So, all we have to do is figure out what affects the angle of attack of a propeller.

Propeller Angle of Attack

The diagram to the left shows the two blades on a typical propeller. Some propellers have more than two blades but all the concepts developed here will still apply.

 

Each blade cross-section is moving along an arc around the crankshaft as well as traveling forward. As a result its motion is a helix.

Before we consider the full helix motion let us look at the simpler case where the engine is running but the aircraft is not moving. (For example the pilot is standing on the brakes while running the engine up, just prior to a short field takeoff.)

The diagram to the left defines the propeller blade angle as the angle between the chord of the propeller airfoil and the arc of rotation (i.e. 90 degrees to the crankshaft.) On a constant speed propeller this angle is variable. On a fixed pitch propeller it is fixed.

The rotational velocity is the speed of rotation, which depends upon the rpm (n) of the engine and the diameter (D) of the propeller blade (the green vector in the diagram.)

In our example there is no forward speed. Therefore, the blade angle and the angle of attack are the same.

 

Effect of TAS on Propeller Angle of Attack

As shown in the diagram to the left, when the aircraft moves forward (TAS vector) the propeller blade has two velocity vectors, the rotational velocity and the TAS

The important things to note are:

  1. Propeller angle of attack Decreases as TAS increases
  2. Propeller angle of attack Increases as rotational velocity increases (rpm x Diameter increases)

We therefore know that the thrust produced by the propeller, which is nothing more than lift by another name, will decrease as the TAS increases because the propeller will be operating at a smaller angle of attack. This will reduce the coefficient of lift for the propeller and thrust will drop off.

When the pilot increases rpm the angle of attack of the propeller will increase. Thus, thrust will increase and the aircraft will accelerate.

Propeller Efficiency

As we learned before, any given wing will have a certain angle of attack at which it if most efficient. This will be true for the propeller as well. It is after all just a wing flying around in a helix pattern.

Since the angle of attack of the propeller depends on both rpm, diameter and TAS, the propeller efficiency will vary according to the ratio of these factors. The ratio Velocity/rpm x diameter is called the Advance Ratio. The formal definition of advance ratio is:

where J is Advance ratio, n is rpm and D is propeller diameter, V is TAS.

The propeller efficiency of a fixed pitch propeller will be a maximum at only one advance ratio, as shown in the diagram to the left.

The most efficient J depends upon the propeller blade angle. Course propellers (large blade angles) will be more efficient at larger advance ratios. Fine pitch propellers will be more efficient at small advance ratios.

 

When choosing a fixed pitch propeller an aeronautical engineer usually chooses one, which is optimum for cruise. However, s/he might choose one, which is optimum for climb if designing a seaplane, tow plane etc.

With a fixed pitch propeller, getting the ideal advance ratio while also keeping the aircraft's wing at the ideal angle of attack for best range will be almost impossible. That is why constant speed propellers are desirable for cross-country airplanes.

The diagram to the left shows how the efficiency varies with different propeller blade angles.

With a constant speed propeller the blade angle will vary from a small angle to a large angle. (The low and high pitch stops.) This allows the propeller to be efficient (i.e. operate at the optimum angle of attack) at a variety of advance ratios.

 Available Thrust Horsepower

Earlier we defined propeller efficiency:

Therefore:

THP = h x BHP

This results in a THP available curve as shown to the left.

It is worth noting that since BHP is a constant the THP curve will have the same shape as the propeller efficiency curves examined earlier. These in turn are the same shape as the L/D vs. CL curve.

 

Text Contents ] Chapter Contents ] Overview ] Definitions of Terms ] Fuel Flow vs Velocity Graphs ] L/D Ratio and Glide Performance ] Specific Fuel Consumption ] Jet Aircraft Range and Endurance ] Cruise Control ] Propeller Aircraft Range and Endurance ] [ Engine and Propeller Efficiency ] Range and Endurance Summary ] Climb Performance ]