Installation Thrust#
The engine data reported by any manufacturer is usually for an “uninstalled” configuration i.e. engine performance is computed when it is not integrated into an airplane. Hence, there is usually some loss of power/thrust when engine is installed on an airplane due to interference. This loss of power/thrust needs to be determined and is usually termed as installation effects. Refer to Chapter 13 in Raymer for a detailed discussion about installation effects and how the power/thrust can be calculated in an “installed” configuration.
Following are some quantities which are used for the analysis of propeller-based propulsion system (based on Section 13.5-13.7 in Raymer). The advance ratio (\(J\)) is the ratio between the forward speed of airplane and the tip speed of the propeller. It denotes how fast an airplane is flying as compared to the propeller speed. It is given as
where \(V\) is the forward velocity, \(D\) is the propeller diameter and \(n\) is the rotation speed. To account for the installation effects, \(J\) can be updated using
where \(S_c\) is the maximum frontal cross-section area of engine cowling behind the propeller. For the example airplane, \(S_c\) is estimated using the engine width and height obtained earlier.
The power coefficient (\(c_P\)) and thrust coefficient (\(c_T\)) are dimensionless forms of power and thrust (similar to drag coefficient) which are used in performance charts of propeller-based propulsion system. They are given as
where \(\rho\) is the density, and \(P\) and \(T\) are power and thrust, repsectively. If an engine is not turbo-charged, then it will lose power as altitude increases. This can computed using (equation 13.10 in Raymer)
where \(\sigma\) is the ratio of density at given altitude and sea-level density.
Finally, the thrust (\(T\)) is computed using
where \(\eta_p\) is the propeller efficiency. Computing static thrust is useful when the airplane is starting its ground-roll for takeoff or when it is moving at low-speeds. The propeller efficiency is reduced due to the formation of shock waves at the propeller tip, and hence, should be corrected if the airplane is going to fly at high-speeds.
Furthermore, one should account for the drag caused by the propulsion system. These usually include scrubbing drag, cooling drag, and miscellaneous engine drag (drag due to auxilliary system required for operating a piston-powered engine). Hence, the thrust computed should be adjusted to account for this drag. One can either use equations for estimating these drags (equation 13.21-13.23 in Raymer) or use an historical estimate for thrust correction due to these drag values. Based on the recommendations in Raymer, it is assumed that the thrust is reduced by 8% due to the drag associated with propulsion system.
NOTE: Since the drag due to the propulsion system is accounted here, it should not be included while perfomring drag build-up for the airplane in aerodynamics section
Based on the above equations, static thrust can computed as follows (based on Section 13.6 in Raymer):
Determine \(\rho\) based on altitude, propeller diameter \(D\) (known), and engine power \(P\) (known)
Update power \(P\) to account for increase in altitude, if required
Calculate \(c_P\) using above formula
Use Fig. 13.11 to estimate the ratio \(c_T/c_p\)
Use static thrust equation to compute thrust
Use the thrust correction factors to compute final thrust
Based on the above equations, forward flight thrust can computed as follows (based on Section 13.6 in Raymer):
Determine \(\rho\) based on altitude, propeller diameter \(D\) (known), and engine power \(P\) (known)
Update power \(P\) to account for increase in altitude, if required
Calculate \(c_P\) using above formula
Compute advance ratio \(J\) using above equation
Update the value of \(J\) based on the installation effects
Use Fig. 13.12, \(J\), and \(c_P\) to compute propeller efficiency \(n_p\)
Update propeller efficiency, if required
Compute thrust using forward flight equation
Use the thrust correction factors to compute final thrust
NOTE: If available, performance charts and static test data should be used for forward flight and static thrust calculations.
This outlines how the thrust can be computed for a propeller-based propulsion system. Next section provides an example thrust calculation for the example airplane.