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Aviation History
1917
1917 - 1196.PDF
NOVEMBER 15, 1917. Let us write X for the exponential e T for convenience,then:— \?\~- h1=H(i-X) •'••"-. :,:;•' .•--, h,=H(i-x*) •.-•• V whence by division 2= i + X .......... but since and 2 ~ f ~-r— "i •which gives the ceiling of the machine in terms of the altitude hi at time / and the altitude h2 at time" 2t. (Note that t may be any time whatever during the climb.) So all we require to calculate the ceiling of a machine, is the altitude after any time, and the altitude after double that time. We will now illustrate the foregoing analysis by a prac- tical example. Observations of a certain aeroplane on a climb test showed the altitude to be related to the time" after start according to the following table :— Time (minutes)—° 2.5 5.0 7.5 10.o 12.5 15.0 17.5 20.0 22.5 Altitude (feet)— o 3300 6150 8730 10760 12610 14190 15530 16650 17600 The ceiling of the machine may be calculated right awaytaking h x as 10760 ft. after 10 minutes and hi as 16650 ft.after 20 minutes. We have H = -i-^Z1 10760 = 23,770 feet.- E5•4526 We may next calculate T, the time constant. The value of the exponential (which we called X for short) is (when t= 10 minutes) -£-i --5474. hence - ^-. loge 5474 whence T 2-3026 x 1 -7383 2-3026 x =• -2617 10 i6*6o minutes. 2-3026 x'2617 The initial rate of climb . = ceiling _ 23770 ~ ••-" time constant 16-60 = 1432 feet per minute. Having calculated the constants of the climb, we may now write down the equations for the altitude at any time, the rate of climb at any time, and the rate of climb at any alti- tude. They are respectively :— / L-) : • -•.-- \i — e 16-60/23770 r -= 1432 e — = 23770 - t and 1660 .From the first two equations the altitude and rate of climb at any time t are calculable and the figures for the altitude are found to agree closely with the table already given, so far as this table goes. We give below a table calculated from these two equations, also a table showing rate of climb at various altitudes. The results are also plotted in the accom- panying curves. ! - . Time (minutes)— o 2.5 5.0 7.5 Altitude (feet)— o 3320 6180 8640 10760 12575 14140- Rate of Climb (feet pejr minute).— 1432 1232 1060 911 Time (minutes)— 17.5 20.0 22.5 25.0 Altitude (feet)— 15485 16645 17640 18500 19240 19870 Rate of Climb (feet per minute)— 499 429 369 10.0 12-5 15-0 784 27-5 674 30.0 580 273 235 -5474- Altitude (feet)— o 2000 4000 6000 80000 10000 Rate of Climb (feet per minute)— 1432 1311 1191 1070 950 829 Altitude (feet)— 12000 14000 16000 18000 20000 Rate of Climb (feet per minute)— 709 588 468 348 227 . A COLD JOB.—A German seaplane on its return from a flight over the North Sea in winter. 1196
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