Question

2. Center-of-gravity (cg) location is critical for airplane stability. To get the "empty' cg location, the Piper J-4 Cub pictured below was leveled and put on three scales (one under each wheel). For this application, the "empty configuration included full fuel, but no pilots or baggage. The top two scale readings (in pounds) are for the two main wheels, and the bottom scale reading is for the tail wheel. 436 eeeeeee In the diagram below, the datum is defined to be the leading edge of the main wing. The distances from the datum to the pilots' seat, baggage compartment, main wheel, tail wheel, and fuel tank are shown. The main-wing mean aerodynamic cord (MAC) is 63 inches. fuel tank baggage 300 ORAES HANES WEELS 325 182.5 datum a. What is the "empty weight? (4 points) b. What is the "empty cg location in inches aft of datum? (7 points) C. What is the "empty cg location in %MAC? (5 points) d. Assume the pilot weighs 180 pounds and the co-pilot weighs 170 pounds, what is the cg location in inches with the crew and full fuel? (10 points)

Answer 1

Solution Given that 5 The main-wing mean aerodynamic cord (MAC) = 63 in 42" R 27866 YILI fuel tank a Ht seat baggage 800E 4 TIRES MUMER HVORAULIC BRAKES HAYES WHEELS 3.25" 182.5" ANS datum (a) : To find the Empty weight- Total Emply Weight = 436+449756 aquilo (b) To find the Emply gg location in inches aft of datum:

Idealising the aircraft as an overhanging beam as Shown belowo. the weight of aircraft is assumed as uniformly distributed load (UDL): หa” หงาย datum. sed Seen Hank in solb soll Weight Lemmotospornabomberopera empty aircraft Bisolb tailuted main wheel whach ! k 182.5" location of ca from point B is found by taking. moment about B R (182-523-25) = frotas 49, 885*179.25 = Quix $2= 168.58) ..ca distance from datum = 182.5 - 168.58 = 13.91"

(o: To And the empty location cg locatio in Y. MACE AC: 13.9) 63 = 22% . The pilot weight =180 pounds The co-pilot weight = 170 pounds pilots weight is added p= 180 +170 p=350 lb Reaction at A&B are: Rat R2 = 850+944 =1291 26 Rat Rę = 120120 Tating moment about_8! RA (182.5-3-25) = qui x 168.58+350x1182.5—28) TRA: 1196.427 .. The moments produces by two seperate loads can be Equated to moment pooduced by. resultant load acting - at CG (vanignois theorem)

1196.42 * (182.5-3.25) = 1291x12. 13=166.11.] New IG = 182.5–166.11 E16-38"] solb baggage is added. RATRE = 350+941450 RAT RB = 134116 Moment about B:- -23 so(1828-4 %[ PS-3-45) - 4:41 8 68-S8 +3Softe 29 = 123S-3310] 1236.33x(182235-3-25) = 1341% 129: 167.98 New Cg location = 182.5- 164.98. La la-si

$5:- Given 10 gallons = 83.5lbf. Retra = 9u1+350+50+ 83.5 Rat Rę = 1424.5lb Moment about B:- Rox 179.25 = 941 v168.58+350 X 159.5+50 x 139.5 + 83.5 (182.5+10) TRA = 1395.00lb) Po x179.5 = 1424.5 My [?u= 166-96) CG 182.5 - 166.96 [(4= 15-53"} 183. The range of g in Y. MAC - %. MAC in 'd' = 16.38 = 26% 63 Y MAC in f = 18.53 = 24.64

In configuration 'd. CG is Alt of datum In configuration 'f' CG is Alt of datum