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Weight Estimation Aircraft weight, and its accurate prediction, is critical as it affects all aspects of performance. Designer must keep weight to a minimum as far as practically possible. Preliminary estimates possible for take-off weight, empty weight and fuel weight using basic requirement, specification (assumed mission profile) and initial configuration selection.
1. Take-off weight (WTO) –
(Roskam method) Note that other methods (e.g. Raymer) use slightly different terminology but same principles.
WTO = WOE + WF + WPL Where: WOE (or WOWE ) = operating weight empty WF = fuel weight WPL = payload weight Operating weight empty may be further broken down into: WOE = WE + Wtfo + Wcrew
Where: WE = empty weight Wtfo = trapped (unusable) fuel weight Wcrew = crew weight
Empty weight sometimes further broken down into: WE = WME + WFEQ Where: WME = manufacturer’s empty weight WFEQ = fixed equipment weight (includes avionics, radar, air-conditioning, APU, etc.)
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2. Preliminary Weight Estimation - Overview
• All textbooks use similar methods whereby comparisons made with existing aircraft. • In Roskam (Vol.1, p.19-30), aircraft classified into one of 12 types and empirical relationship
found for log WE against log WTO. • Categories are:
– (1) homebuilt props, (2) single-engine props, (3) twin-engine props, (4) agricultural, (5) business jets, (6) regional turboprops, (7) transport jets, (8) military trainers, (9) fighters, (10) military patrol, bombers & transports, (11) flying boats, (12) supersonic cruise.
• Most aircraft of reasonably conventional design can be assumed to fit into one of the 12
categories. • New correlations may be made for new categories (e.g. UAVs). • Account may also be made for effects of modern technology (e.g. new materials) – method
presented in Roskam Vol.1, p.18. • Raymer method uses Table 3.1 & Fig 3.1 (p.13).
Preliminary Weight Estimation Process
• Process begins with guess of take-off weight. • Payload weight determined from specification. • Fuel required to complete specified mission then calculated as fraction of guessed take-off
weight. • Tentative value of empty weight then found using:
WE(tent) = WTO(guess) – WPL - Wcrew - WF - Wtfo • Values of WTO and WE compared with appropriate correlation graph. • Improved guesses then made and process iterated until convergence.
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• Note that convergence will not occur if specification is too demanding
Initial Guess of Take-Off Weight • Good starting point is to use existing aircraft with similar role and payload-range capability. • An accurate initial guess will accelerate the iteration process.
Payload Weight & Crew • WPL is generally given in the specification and will be made up of:
– passengers & baggage; cargo; military loads (e.g. ammunition, bombs, missiles, external stores, etc.).
• Typical values given in Roskam Vol.1 p8. • Specific values for some items (e.g. weapons) may be found elsewhere.
Mission Fuel Weight • This is the sum of the fuel used and the reserve fuel.
WF = WF(used) + WF(res) • Calculated by ‘fuel fraction’ method.
– compares aircraft weights at start and end of particular mission phases. – difference is fuel used during that phase (assuming no payload drop). – overall fraction is product of individual phase fractions.
Simple Cruise Mission Example
1. start & warm-up 2. taxi 3. take-off 4. climb 5. cruise
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6. loiter 7. descend 8. taxi
• Fuel fractions for fuel-intensive phases (e.g. 4, 5 & 6 above) calculated analytically. • Non fuel-intensive fuel fractions based on experience and obtained from Roskam (Vol 1, p12),
Raymer, etc.
• Using Roskam’s method/data for a transport jet (Vol.1, Table 2.1):
Phase 1 (start & warm-up)
W1/WTO = 0.99.
Phase 2 (taxi)
W2/W1 = 0.99.
Phase 3 (take-off)
W3/W2 = 0.995. Phase 4 (climb) For piston-prop a/c:
For jet a/c:
where: Ecl = climb time (hrs), L/D = lift/drag ratio, cj is sfc for jet a/c (lb/hr/lb), cp is sfc for prop a/c (lb/hr/hp), Vcl = climb speed (mph), ηp = prop efficiency, W3 & W4 = a/c weight at start and end of climb phase.
• Initial estimates of L/D, cj or cp, ηp and Vcl made from Roskam or Raymer databases for appropriate a/c category.
• Alternatively, use approximations, e.g. from Roskam Vol.1, Table 2.1 (W4/W3=0.98 for jet transport, 0.96 to 0.9 for fighters).
Phase 5 (cruise)
• Weight fraction calculated using Breguet range equations. • For prop a/c:
• For jet a/c:
• These give the range in miles.
4
5
lncrclj cr
V L WR
c D W
=
3
4
1lncl
clj cl
WLE
c D W
=
3
4
1375 lnp
clclcl p cl
WLE
V c D W
η =
5
• For jet a/c, range maximised by flying at 1.32 x minimum drag speed and minimising sfc. – wing operates at about 86.7% of maximum L/D value. – cruise-climbing can also extend range.
• For prop a/c, range maximised by flying at minimum drag speed and sfc. – wing operates at maximum L/D value.
Initial Estimates of Lift/Drag Ratio (L/D) Using Roskam (Table 2.2 – selected values cruise loiter
Homebuilt & single-engine 8 - 10 10 - 12 Business jets 10 – 12 12 - 14
Regional turboprops 11 – 13 14 – 16
Transport jets 13 – 15 14 - 18
Military trainers 8 – 10 10 - 14
Fighters 4 – 7 6 – 9
Military patrol, bombers & transports 13 – 15 14 – 18
Supersonic cruise 4 - 6 7 – 9
Specific Fuel Consumption Initial estimates of cj (lb/hr/lb)
• Using Raymer (Table 3.3):
cruise loiter
Turbojet 0.9 0.8
Low-bypass turbofan 0.8 0.7
High-bypass turbofan 0.5 0.4
• Roskam Vol.1 Table 2.2 (p.14) gives a/c category-specific values Jet aircraft - Initial estimates of cj (lb/hr/lb)
cruise Loiter
Business & transport jets 0.5 - 0.9 0.4 - 0.6
Military trainers 0.5 - 1.0 0.4 - 0.6
Fighters 0.6 - 1.4 0.6 - 0.8
Military patrol, bombers, transports, flying boats 0.5 – 0.9 0.4 - 0.6
Supersonic cruise 0.7 – 1.5 0.6 - 0.8
Prop aircraft - Initial estimates of cp (lb/hr/hp)
• Using Raymer (Table 3.4): cruise loiter
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Piston-prop (fixed pitch) 0.4 0.5
Piston-prop (variable pitch) 0.4 0.5
Turboprop 0.5 0.6
• Take propeller efficiency (ηp) as 0.8 or 0.7 for fixed-pitch piston-prop in loiter.
Prop aircraft - Initial estimates of cp (lb/hr/hp) & ηp • Using Roskam (Table 2.2):
Cruise loiter Single engine 0.5 – 0.7, 0.8 0.5 – 0.7, 0.7 Twin engine 0.5 – 0.7, 0.82 0.5 – 0.7, 0.72 Regional turboprops 0.4 – 0.6, 0.85 0.5 – 0.7, 0.77 Military trainers 0.4 – 0.6, 0.82 0.4 – 0.6, 0.77 Fighters 0.5 – 0.7, 0.82 0.5 – 0.7, 0.77 Military patrol, bombers & transports 0.4 – 0.7, 0.82 0.5 – 0.7, 0.77 Flying boats, amphibious 0.5 – 0.7, 0.82 0.5 – 0.7, 0.77 Phase 6 (loiter)
• Fuel fraction (W6/W5) found from appropriate endurance equation as in Phase 4. • For jet a/c, best loiter at minimum drag speed (maximum L/D value); for prop a/c at minimum
power speed. Phase 7 (descent)
W7/W6 = 0.99. Phase 8 (taxi)
W8/W7 = 0.992. Overall Fuel Fraction (Mff)
• Mission fuel used (WF(used))
• WF then found from equation (5), by adding reserve fuel (WF,res). • This then allows for tentative value for WE(tent) to be found, from eq. (4). • This may be plotted with WTO on appropriate a/c category graph to check agreement with fit. • If not, then process must be iterated until satisfactory. • Two other possible mission phases may need to be considered for certain aircraft:
• manoeuvring • payload drop
Manoeuvring Fuel • Breguet range equation may be used with range covered in turn (R turn) from perimeter length of
a turn (P turn) multiplied by number of turns (N turn).
• For manoeuvre under load factor of n:
• Treated as separate sortie phase with change in total weight but no fuel change.
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1turn
VP
g nπ
= −
turn turn turnR N P=
( )( ) 1F used ff TOW M W= − =
8 7 6 5 34 2 1
7 6 5 4 3 2 1ff
TO
W W W W WW W WM
W W W W W W W W=
7
• Fuel fraction taken as 1 but subsequent phases corrected to allow for payload drop weight change.
• Roskam Vol.1 pp.63-64 gives details. • e.g. if W5 and W6 are weights before and after payload drops:
Worked Example – Jet Transport Specification
Payload: 150 passengers at 175 lbs each & 30 lbs baggage each. Crew: 2 pilots and 3 cabin attendants at 175 lbs each and 30 lbs baggage each. Range: 1500 nm, followed by 1 hour loiter, followed by 100 nm flight to alternate
and descent. Altitude: 35,000 ft for design range. Cruise speed: M = 0.82 at 35,000 ft. Climb: direct climb to 35,000 ft at max WTO. Take-off & landing: FAR 25 field-length of 5,000 ft.
• WPL = 150 x (175 + 30) = 30,750 lbs • Wcrew = 1,025 lbs • Initial guess of WTO required, so compare with similar aircraft:
– Boeing 737-300 has range of 1620 nm for payload mass of 35,000 lbs – WTO = 135,000 lbs.
– Initial guess of 127,000 lbs seems reasonable. • Now need to determine a value for WF, using the fuel fraction method outlined above. • As in earlier example, for a transport jet:
Phase 1 (start & warm-up) W1/WTO = 0.99.
Phase 2 (taxi) W2/W1 = 0.99. Phase 3 (take-off) W3/W2 = 0.995.
6 5 PLW W W= −
5 34 2 15
4 3 2 1TO
TO
W WW W WW W
W W W W W=
8
Phase 4 (climb) W4/W3 = 0.98. The climb phase should also be given credit in the range calculation. Assuming a typical climb rate of 2500 ft/min at a speed at 275 kts then it takes 14 minutes to climb to 35,000 ft.
• Range covered in this time is approximately (14/60) x 275 = 64 nm. Phase 5 (cruise)
• Cruise Mach number of 0.82 at altitude of 35,000 ft equates to cruise speed of 473 kts. • Using eq. (7b):
• Assumptions of L/D = 16 and cj = 0.5 lb/hr/lb with a range of 1500 – 64 (=1436 nm) yield a
value of: W5/W4 = 0.909
Phase 6 (loiter)
• Using eq. (6b):
• Assumptions of L/D = 18 and cj = 0.6 lb/hr/lb. • No range credit assumed for loiter phase. • Substitution of data into eq. (6b) yields:
W6/W5 = 0.967 Phase 7 (descent)
• No credit given for range. W7/W6 = 0.99. Phase 8 (fly to alternate & descend)
• May be found using eq. (6b) again. • Cruise will now take place at lower speed and altitude than optimum – assume cruise speed of
250 kts (FAR 25), L/D of 10 and cj of 0.9 lb/hr/lb. • Gives: W8/W7 = 0.965
Phase 9 (landing, taxi & shutdown)
• No credit given for range. W9/W8 = 0.992. Overall mission fuel fraction (Mff)
• found from eq. (8) (with additional term for W9/W8) = 0.992x0.965x0.99x0.967x0.909x0.98x0.995x0.99x0.99 = 0.796
• Using eq. (9), WF = 0.204 WTO = 25,908 lbs Phase 9 (landing, taxi & shutdown)
3
4
1lncl
clj cl
WLE
c D W
=
4
5
lncrclj cr
V L WR
c D W
=
9
• Using eq. (4): WE(tent) = WTO(guess) – WPL - Wcrew - WF – Wtfo ∴ WE(tent) = 127,000 – 30,750 – 1,025 – 25,908 - 0 = 69,317 lbs
• By comparing with Roskam Vol. 1, Fig. 2.9, it is seen that there is a good match for these values of WE and WTO, hence a satisfactory solution has been reached.
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