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Aviation History
1931
1931 - 0779.PDF
TULY 24, 1931 THE AIRCRAFT ENGINEER SUPPLEMENT TOFLIGHT i j.SOOfc sooo \ Fl(3 4 \ of rate of climb, terminating at the supercharge limit,and from it the time to supercharge limit calculated and compared with the actual time taken. If agreement isnot achieved, the line must be adjusted until its inclina- tion and upward extremity are correct. Above the supercharge limit, the reduction of rate ofclimb may be first considered regular, and a trial line run through the plotted points is drawn and the timestaken off it as before for comparison with actual times. (To be concluded.) A FORMULA FOR THE BUOYANCY OF THE WING FLOATS OF FLYING BOATS AND SINGLE FLOAT SEAPLANES. BY A. R. COLLINS. The hull and aerostructure of a flying boat, or themain float and aerostructure of a single-float seaplane has, in general, a negative transverse metacentricheight in the upright condition so that, in the trans- verse direction, it is inherently unstable. In thiscountry, the conventional method of providing positive transverse stability is by fitting wing floats, and thefollowing note deals wiih a simple formula for obtaining the desirable buoyancy of such floats. Let us first consider the function of a wing float,and how it gives to the aircraft a virtual positive meta- centric height in the transverse direction. Referring tothe sketch, let W = the all-up weight of the flying boat or single-float seaplane. w = the total buoyancy of one wing float. aft = the water-line in the upright condition. CD = the water-line when one wing float is com- pletely submerged. 0 = the angla of heel or roll to submerge completely one wing float. G = the centre of gravity of the complete aircraft. B and B1 = the centres of buoyancy of the hull or main float (with its aerostructure) in the upright and inclined conditions, respectively. M = the transverse metacentre in the upright con- dition, i.e., the point where a vertical line through B1 intersects the line joining B to G. 6M = the transverse metacentric height of the com- plete aircraft in the upright condition. d = the distance from the centre line of the hull or main float to the centre line of a wing float. Since M is below G, the aircraft has a negative GM inthe upright condition, which gives rise to an upsetting nioment when the hull is displaced from the vertical.As BOOH as one wing float touches the water, a rightingttoment is called into play, which gradually overcomes the upsetting moment of the hull and aerostructure,and gives to it a virtual positive metacentric height. Now when one win^ float is completely submerged,the upsetting moment of the hull or main float (with its aerostructure) = W.GZ (where GZ is the perpen-dicular from G on to B'M produced)= W.GM. Sin 0. = H (say) The righting moment of the wing float = w.d. Cos 0 = F (say) .'. The reserve righting moment of the wing float = F - H. Hence the ratio of the reserve righting moment of the wing float to the upsetting moment of the hull or main float = -^ = R (say) • F — H = R.H = R (W.GM. Sin 0) = W (11.GM) Sin 0. i.e., when one wing float is submerged completely, itgives to the aircraft a virtual positive inetaccntric height = B.GM. Now a good empirical rule for the transverse meta-centric height of a twin float seaplane is " Transverse metacentric height in feet = "v'Wwhere W is the all-up weight of the seaplane in pounds." Hence, to make the stability of a flying boat orsingle-float seaplane consistent with good twin-float sea- plane practice, the virtual positive metacentric heightin feet, with one wing float just submerged should = *\/W. In other words, one should aim at the samemeasure of positive transverse static stability for flying boats and single-float seaplanes, as has been foundadequate and desirable for twin-float seaplanes. Now let h = the negative metacentric height of thecomplete aircraft in the upright condition. \h will be practically constant for values of 0 up to about 10°,which will cover the range of angles of heel or roll, to submerge completely one wing float, for most flyingboats and single-float seaplanes.] When one wing float is just submerged we have (using the same notation as before) upsetting moment of hull or main float (with its aerostructure) = W.fc. Sin 6. Righting moment of the wing float = w.d. Cos 6..'. Reserve righting moment of the wing float = w.d. Cos 6 - W./i. Sin 0. .'. The ratio of the reserve righting moment of the wing float to the upsetting moment of the hull or main float w.d. Cos 8 - W.h. Sin 6 = W.ft. T w.d. Cot 6 W.fc. - 1 = R (say). Now it has already been shown that the virtual positive metacentric height of the complete aircraft with a wing float just submerged = R.Ti. and this should be = '/W
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