Aircraft Conceptual Design Lecture 5: Initial Sizing PDF

Aircraft Conceptual Design Lecture 5: Initial Sizing Engine sizing Aircraft can be sized based on an existing engine or a new design engine. • Existing engine would have a fixed size and thrust, and is referred to as fixed engine. • A new engine could be designed to required size and thrust, and...

Aircraft Conceptual Design Lecture 5: Initial Sizing Engine sizing Aircraft can be sized based on an existing engine or a new design engine. • Existing engine would have a fixed size and thrust, and is referred to as fixed engine. • A new engine could be designed to required size and thrust, and is called rubber engine. The design may begin with a rubber engine, but in later stages, a close existing engine may be chosen, or, engine companies may be contacted to design engine that suits the needs. • Developing a new engine is very expensive, so designing with an existing engine (or group of engines) in mind is recommended. 2 Refined sizing equation – rubber engine In the crude sizing calculations, we used: where Now we consider a fixed and dropped payload separately: We will find the TOGW through iteration. 3 Empty weight fraction – rubber engine We / W0 is now calculated based on more accurate historical data. 4 Fuel weight – rubber engine For each mission segment, fuel burned is W fi Wi 1  Wi 1  Wi Wi 1 W fi  Wi 1  Wi  W   W fi  1  i Wi 1  Wi 1  The total mission fuel then becomes Taking into account reserve fuel (5%) and trapped fuel (1%), total aircraft fuel is calculated as : Mission segment weight fractions For the first segment of engine start, taxi and takeoff, a W1 historically good assumption is:  0.97  0.99 W0 5 Mission segment weight fractions For climbing and accelerating, use the following approximations: Where M is the ending Mach number, starting at Mach 0.1. Example: Find weight fractions for accelerating from Mach 0.1 to Mach 2.0, where W2 is the weight fraction at Mach 0.1, W3 is that at Mach 0.8, and W4 is that at Mach 2.0. W3 W4 W4   W2 W3 W2 W3 W4 2  1.0065  0.0325  0.8  0.9805  0.991  0.007  2.0  0.01  2.0   0.937 W2 W2  W4 0.937   0.956 W3 60.9805 Mission segment weight fractions For cruise flight, use the equation from lecture 2. For jet aircraft: Wi 1 e Wi where R is range, C is specific fuel consumption, and V is velocity. For propellers, C is calculated from the table below. Substituting, Wi 1 Wi e   RC power    p ( L D)      e   RCbhp     550 p ( L D )    Where ηp is propeller efficiency. During cruise and loiter, L=W, hence L W 1    D D D W where wing loading is specific to the condition under analysis, not takeoff segment. 7   RC     V ( L D)  Mission segment weight fractions For loiter, similar to lecture 2 and climb conditions slide, For specified-duration fuel burn segments (combat, aerobatics etc.), Where d is time duration in minutes. T/W is combat weight and thrust, not takeoff. For descent for landing: For landing and taxi back: 8 Sizing review 1. Start with design objectives and mission 2. Decide on wing geometry (determine e) and initial layout 3. Determine wetted area ratio and CD0 using wing geometry and initial layout 4. Estimate thrust-to-weight ratio and wing loading 5. Using an engine SFC, calculate mission segment weight fractions 6. Guess a value for takeoff gross weight, and calculate weight after each mission segment. Weight will decrease due to fuel burn and/or weight drop. 7. Add up total fuel burned, plus reserve and trapped. Use that and empty weight to calculate new W0 8. Iterate until convergence 9 10 Fixed-engine sizing With power supply fixed, designer must consider either range or performance as a dependent parameter. If range is dependent (allowed to vary as the aircraft is sized), use T/W and engine data to calculate performance capabilities. TOGW is : where N is number of engines. • If the TOGW is known, range can then be determined using • Iterate as follows: Use the same known TOGW as your guess in each iteration, but vary the range for one or more cruise segments until resulting W0 equals your TOGW. 11 Fixed-engine sizing If range is a design parameter, then performance must be dependent. T/W will depend on fuel requirements and engine capabilities. Weight equation is used again, but this time T/W varies. Weight fraction for a combat mission cannot be determined using as before, because it assumes a known (T/W). • Instead, fuel burned is calculated by SFC times thrust times duration: • This weight is treated as a weight drop in weight iterations. • Upon convergence, resulting T/W is used to calculate performance, as discussed before. • If performance requirements are not met, either your design is not good, or the requirements are too tough. 12 Geometry sizing Once the TOGW is known, fuselage length can be estimated using the table. Ratio of fuselage length to max. diameter is called fineness ratio. Subsonic drag is minimum at a fineness ratio of 3.0, but it may not provide enough tail moment, so a tail boom has to be added. Supersonic drag is minimum at 14. Wing area can be found by dividing TOGW by takeoff wing loading. This wing area includes the area inside the fuselage. 13 Geometry sizing The tail generates moments to overcome wing moments. Effectiveness of the tail is related to tail moment arm length times tail area. It has units of volume, therefore called tail volume coefficient. Nondimensionalized vertical and horizontal tail volume coefficients are: where bw is wing span, C w is wing mean chord, L is moment arm, and S is area. L is measured between the quarter-chords of the wing and the tail (see figure) 14 Geometry sizing Lower right table shows typical values for volume coefficients. Tail areas can be calculated using those coefficients and their formulas. Tail arms can be estimated based on fuselage length, see table lower left. Tail arm [% Configuration fuselage length] Front-mounted propeller 60% Engines on wings 50-55% Aft mounted engines 45-50% sailplane 65% 15 Geometry sizing Effect of tail designs on tail coefficients (table on right) Tail type Reduction on volume coefficients All-moving tail 10-15% T-tail 5% H-tail 5% Primary control surfaces are ailerons (for roll), elevator (for pitch) and rudder (for yaw). Aileron area can be estimated from the figure on left. Ailerons extend from 50% to 90+% of span. Flaps are used for increased lift coefficient. • They must have greater span if a large CLmax is required. • They are placed on wings, inboard of ailerons. • Aileron and flap width is about 15-25% of wing chord. One way to have larger flaps is to use smaller ailerons, augmented with spoilers. • Spoilers are plates located forward of flaps on top of the wing, typically behind the max. thickness point. • They are deflected upward onto the flow to reduce wing lift. • Deploying the spoiler on one wing causes a large rolling moment. • They are used on jet transports to increase roll control at low speed, and also to reduce lift, and add drag during landing. 17 High-speed aircraft may have a problem called aileron reversal. • The air loads on the aileron may be so high that the wing itself is twisted. • At some speed, the rolling moment from the twisting wing becomes greater than the rolling moment of the aileron, so the aircraft rolls towards the opposite way. • To avoid this, transport jets use additional inboard ailerons for high-speed control. Spoilers can be used as well. Elevators and rudders begin near fuselage, and extend to 90% of tail span. See Table 6.5 on page 125 of your textbook for tail control surface guidelines. 18 Some high-speed aircraft use • rolling tails (horizontal tails capable of being deflected nonsymmetrically) to avoid aileon reversal • all-moving tails for more control Aileron and flap chord lengths are usually 15-25% of wing chord. For structurally sound wings and tails, control surfaces are tapered in chord by the same ratio as the wing or tail surface (see figure) 19