Weight Estimation_002.pdf

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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.

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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=

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• 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=

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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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