Estimate Gross Takeoff weight, empty weight, mission fuel weight Example problem

Question

Estimate Gross Takeoff weight, empty weight, mission fuel weight

Example problem
Pg 55: Airplane design part 1 by Jane Roskam

Please show steps

Design a subsonic jet transport airplane to satisfy the following mission specifications Payload: Crew Range Altitude Cruise speed: Climb: Take-off and Landing 291 Passengers Two pilots and three cabin attendants at 175lbs each and 30 Ilbs baggage eaclh 7550 nm following by 30 minutes loiter 36,000 ft M=0.80 at 36,000 ft Direct climb to 36,000 ft. at maximum take-off weight WTo FAR 25 fieldlength, 6930 ft. at an altitude of 4000 ft and a 99.5° F day. Landing performance at about WL -0.81 WTO Two turbofans Engines: Certification base FAR 25

Explanation / Answer

Given that,

     291 passengers , two pilots

Range = 7550 nm = 7550 X 10-9 m

Time = 30 min = 30 X 60 = 1800 s

R = VT

   V = 7550 X 10-9 / 1800

      = 4.19 nm/s

   Lift weight = cl ( 0.5 r V2 ) A

      r = altitude =36000 ft = 10972.8 m

    WL = 0.5 ( 0.5 X 10972.8 x 4.19 x 10-9 ) 2.5 X 105

         = 287 lbs

Gross take off weight = 0.81 X 287 = 232.7

b) Empty weight =?

      Gross weight - Lift weight = Empty weight

       287 - 232.7 = 54.3

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