Initial Maximum Cruise Speed
Civil aircraft maximum speed is executed in HSC in a steady, level flight when the available thrust equals the aircraft drag. The first task is to compute drag at the maximum cruise speed and then check whether the available thrust (at the maximum cruise rating) is sufficient to achieve the required speed. Sometimes, the available maximum cruise thrust is more than what is required; in that case, the engine is adjusted to a slightly lower level. The LRC schedule is meant to maximize range and is operated at a lower speed to avoid the compressibility drag rise. Section
13.5.6 explains the worked-out example.
13.4.3 Payload Range Capability
Finally, a civil aircraft must be able to meet the payload range capability as specified by the market (i. e., customer) requirements. The mission range and fuel consumed during the mission are given by the following two equations:
mission range — Rclimb + Rcruise + Rdescent (13.22)
mission fuel — Fuelclimb + Fuelcruise + Fueldescent (13.23)
mission time — Timedimb + Timewise + Timedescent
The method to compute fuel consumption, distance covered, and time taken during a climb and a descent is discussed in Section 13.4.3. In this section, the governing equations for cruise range (Rcruise), cruise fuel (Fuelcmise), and time taken during cruise are derived.
Let Wi — aircraft initial cruise weight (at the end of a climb) and Wf — aircraft final cruise weight (at the end of a cruise). Then:
fuel burned during cruise — Fuelcruise — Wi – Wf (13.24)
At any instant, rate of aircraft weight change, dW — rate of fuel burned (consumed). In an infinitesimal time dt, the infinitesimal weight change, dW — sfc x thrust (T) x dt, or:
dt — dW/(sfc x T)
Integrating Equation 13.25 gives the time taken for the Rcruise. At cruise, T — D and L — W.
In Equation 13.25, multiply both the numerator and the denominator by weight, W, and then equate T — D and W — L.
Equation 13.25 reduces to:
_ / W (dW_ / М /dW
t — sfc T W — sfc D W
The elemental range:
Therefore, the range covered during cruise (Remise) is the integration of Equation 13.27 from the initial to the final cruise weight. At cruise, V and sfe remain nearly constant. Using the midcruise L/D, the change in L/D can be ignored and taken out of the integral sign:
The value of ln(Wi/Wf) = ki_range varies from 0.2 to 0.5; the longer the range, the higher is the value.
In Equation 13.28, the terms Wi and Wf are concerned with fuel consumed during cruise and the term sfe stems from the matched-engine characteristics. The other terms (VL/D) are concerned with aircraft aerodynamics. Aircraft designers aim to increase the VL/D as best as it is possible to maximize the range capability. The aim is not just to maximize the L/D but also to maximize the VL/D. Expressing this in terms of the Mach number, it becomes ML/D. To obtain the best of engine-aircraft gain, it is to maximize (ML)/(sfcD).
Specific range (Sp. Rn) is defined as range covered per unit weight (or mass) of fuel burned. Using Equation 13.28:
Sp. Rn = Reruise/cruise fuel = [kj_range x (VL)/(sfeD)]/(Wi – Wf) (13.29)
The cruise fuel weight (Wi – Wf) can be expressed in terms of the MTOW and varies from 15 to 40% of the MTOW; the longer the range, the higher is the value. Let k2_range = ki^ange/(0.15 to 0.4). Then, Equation 13.29 reduces to:
Equation 13.30 provides insight to what can maximize the range; that is, a good design to stay ahead of the competition:
1. Design an aircraft to be as light as possible without sacrificing safety. Material selection and structural efficiency are key; integrate with lighter bought-out equipment.
2. Use superior aerodynamics to lower drag.
3. Choose a better aerofoil for good lift, keeping the moment low.
4. Design an aircraft to cruise as fast as possible within the Mcrit.
5. Match the best available engine with the lowest sfe.
However, these points do not address cost implications. In the end, the DOC dictates the market appeal and designers must compromise performance with cost. These points comprise the essence of good civil aircraft design, which is easily said but not so easy to achieve, as must be experienced by readers.
Equation 13.25 can be further developed. From the definition of the lift coefficient, CL, the aircraft velocity, V, can be expressed as follows:
Substituting in Equation 13.25, the cruise range, Rcruise, can be written as:
R fWi 1 I 2W / L dW ПГ rW 1 / УCl dW
Rmise Wf sfc P SwCl D W p Sw Wf sfc CD JW
As mentioned previously, over the cruise range, changes in the sfc and L/D typically are minor. If the midcruise values are taken as an average, then they may be treated as constant and are taken outside the integral sign. Then, Equation 13.31 becomes:
This equation is known as the Breguet range formula, originally derived for propeller-driven aircraft that had embedded propeller parameters (jet propulsion was not yet invented).
The LRC is carried out at the best sfc and at the maximum value of VCL/CD (i. e., L/D) to maximize range. Typically, the best L/D occurs at the midcruise condition. For a very high LRC (i. e., 2,500 nm or more), the aircraft weight difference from initial to final cruise is significant. It is beneficial if cruise is carried out at a higher altitude when the aircraft becomes lighter, which can be done either in a stepped altitude or by making a gradual, shallow climb that matches the gradual lightening of the aircraft. Sometimes a mission may demand HSC to save time, in which case Equation 13.29 is still valid but not operating for the best range.