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Aviation History
1928
1928 - 0036.PDF
JANUARY 19, 1928 SPEED FORMULAE FOR HANDICAPPING IN our Editorial Comment last week we referred to the subject of Handicap Formulae for Racing, mentioning that the formula which it is suggested to use this year (although the actual formula has not yet been definitely settled upon), is based upon that suggested by Mr. C. C. Walker in THE AIR- CRAFT ENGINEER of September 22, 1927. Our reference to this year's formula has created considerable interest, and it may thus be acceptable to our readers if we refer to the subject in rather more detail this week. First of all, it may be recollected that Mr. Walker's original formula for speed was V = K x B.H.P.• ;-. where K had theSpan2 value 261-3 and the "Span" for handicapping purposes was taken, in the case of a biplane, as Sj + • 125 S2, Sj being the larger and S2 the smaller span. In order to avoid the necessity of referring back to the September 22, 1927, issue of THE AIRCRAFT ENGINEER (Technical Supplement to FLIGHT), we reproduce Mr. Walker's chart this week. On it King's Cup would fare under the new formula now suggested. Such few examples as have been published in FLIGHT indicate fairly good agreement. For instance, on the new formula the Hawker " Cygnet," assuming a b.h.p. of 32, would be credited with a speed of 78-5 m.p.h. The Westland " Widgeon III " with " Cirrus II " engine would be estimated for handicap purposes to do 102-5 m.p.h. The de Havilland D.H.61, with a span of 52 ft. and a b.h.p. of 450 would be assumed to do 120 m.p.h., and the Gloster " Gamecock II," with " Jupiter " engine, would be credited with 180 m.p.h. The approximation in these cases is seen to be reasonably good, except in the last machine. " Wing power," i.e., b.h.p. per square foot of wing area, is another basis that might be adopted. Mr. Walker has pointed out that this might lead to some rather grotesque aspect ratios by encouraging designers to adopt large chord so as to get credited with the extra area. In this connection it may be of interest to include a reference to some high-speed formulae given by Prof. E. P. Warner in his book " Aero- 1-20 100 0-80 fi-60 0-20 0 TTTT -^ Till TTTT ~HP IIII IIII \ \ \ IIII TTTT \ \ y \ \ TTTT STAND/Cirrus i \ \ \ \ \ *PTER IIII TTTT TTTT 0. IIII 0. H,sr , STANDARD XriO"(Cirrus MSKl «O'MOTH* 1 |7 1*1) • 1- \ "AN EC u\ y \ "/B/Xf OOACTYL*(fc/X 1 I i 1 I I I I 1 \ \ TTTT n H 50 W /* \ N \ S TTTT C 3KKER \ OTH"-C TTrr ,H."HEF FSE ( \ 54. 2 H. CLE "WIDGEON BI CLEANED NCR OP RACE.-M6T CIRRUS (burnt) CLI irpt) till IIII till TTTT TT NIMBUS ^ tCULES" 1 s \ \ BR .* WIT 1AP / . s II IT TINSY r VIXEN - B :GUET 19 Be M RA.F. 3AEI ANED UP UP 'MOTH' :ANED UP i 11 i 1 I i KINGS U BEST LA( 1 | 1 1 I 1 TTTT 'E F*- ^^ .8tlW iSTLAJ N3INE IP 1927 5 SPEC iiii TTTT •-ACR 'SPEW > III! TTTT AL DE 3-KIN« i I 1 I TTTT VtH 19 >SCUP IIII TTTT CURTI! 13 1927 -| IIII TTTT S RjC I i i i 11 IT1 LAND IIII TTTT IIII IIII IIII TTTT **\ I M I III I III I I I 1 1Mi l III I III I III I • 11 r 40 60 80 100 ' 120 140 160 180 200 220 240 260 280 TOP 5PEED-M.P.H. SIMPLE FORMULAE FOR ESTIMATING TOP SPEED : Above is a reproduction of Mr. Walker's original chart, based on the formula V = Kx BH-P- where K has a value of 261 3 and the span S = Sx +0 125S2, Sx being larger and S2 smaller span of a biplane. Mr. Walker plotted the known speeds of a number of machines from last year's King's Cup race. It will be seen that, gener- ally speaking, the formula tends to over-estimate the speeds, especially in the case of high-power, small span machines. Possibly as a result of this fact, it is suggested that the formula for this year's race should be slightly modified. Thus, the value of K, it is suggested, should be reduced to 260, while the biplane allowance has been increased to -265 S2. Both alterations tend towards lower handicap speeds. We referred briefly last week to the reasons which had led Mr. Walker to adopt span, or rather " span squared," instead of wing area, and it would seem that his views have been accepted as a basis for discussion of the subject. The new suggested formula V= 260 X B.H.P.-= £-, the equivalent span being Sx + -265 S2, will tend to shift the curve of Mr. Walker's chart slightly towards the left, and would thus slightly under- estimate the speeds of some machines, and would reduce the amount of over-estimating others. Unfortunately, we have not in our possession sufficient data of an adequate number of machines to enable us to judge as to how certain machines built since last year's race for the dynamics." Thus, in chapter XVI Warner gives the following 3 /p formula for top speed : Vmax. = Kj A/ ^T, where K has an average value of 124, the speed V being given in m.p.h., and P and S indicating b.h.p. and wing area respectively. The author points out that a comparison between the result given by this equation (58) and the actual measured figures for a number of machines of various characteristics suggests the possibility of getting better agreement between the two by a modification in the exponent used. That has been done in the left-hand chart which we give on p. 37. In this, the full line /Py39 represents the formula V = 127 -j . The right-hand curve has K = 140 and the left-hand curve K = 114. Prof. Warner points out that for the 65 machines covered by the /p\-39 chart, equation (59), which is as follows : V = 1271 _ j gives the speed with an error of less than 10 per cent, except *"- 10 landplanes and four seaplanes (the seaplanes arefor 36
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