Re: Aviation Algebra -- Practical Examples

Physics problems in motion - F=MA; acceleration for takeoff,
deceleration for landing, Wheel brakes good below 70 knots and antikid
will give a decelration effect of about 80% of aircraft weight on a dry
runway. Rule of thumb - full reverse thrust gives about 40% of the
engines maximum rated forward thrust for stopping. Level turn angle of
bank vs G; G= sec bank angle. Radius of action; throw in wind to make
it harder. harder yet drop external load at max radius, cruise out slow
burning more fuel, cruise back high and faster burning less fuel.
Nominal fighter aircraft - starting fuel 18000 pounds, 6000 burned
climbing to cruise atitude of 25000 covering 60 miles, cruise out at
..78M burning 8000 pounds per hour, drop external load taking 5 minutes
to do so and burning 2000 pounds of fuel, climb to 35,000 covering 30
miles in 4 minutes burning 7000 pounds per hour, cruise back home at
..87M burning 7000 pounds per hour. Descent covers 35 miles burning 150
pounds of fuel. Desired fuel on pitch out to land is 1500 pounds.
Throwing a wind into the problem makes things a bit harder, especially
if the wind is not along the direction of flght and even harder if
there are different winds at the two altitudes (two unknowns here).
More data - in an axial flow turbine engine thrust varies as the cube
of the rpm. Typical idle rpm around 68%, full rated thrust at 100%. (=
7500-9000 rpm). Fuel efficiency varies between engines. Old ones run
about .8-1.1 pound fuel per pound thrust per hour. The latest ones are
better, running around .5 or so. FWIW on a GE CF6 turbofan producing
50,000 pounds thrust, 2/3 of the fuel energy goes to drive the
compressors and the fan. IE it's burning '150000 pounds thrust worth'
of fuel but you only get 50K pounds thrust out of it. Work out ;coffin
corner' - critical Mach versus stall speed. Assume 100 KIAS stall and
Mcrit is .87 - what height is that? (Standard day) The Mach number will
vary with the ambient temperature. Taking the square root of the
quotient of ambient divided by standard (absolute temps, of course)
will give you the correction factor to apply to the Mcrit number. Now -
show which is worse, warmer than standard or colder than standard. The
importance is that some aircraft nose down uncontrollably if their
Mcrit is exceeded. Here's a few problems to play with. Have fun. BTW I
taught all this and more to my aviation students.
Walt BJ

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