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"System Mass Integrating Time & Height" © (SMITH) where Performance = Control ©.
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Pressure Interval Temperature C/F
Altitude Elements ZERO WIND TAKEOFF DISTANCE
Liftoff Velocity 54 KIAS
PA(ft) Takeoff 0C/32F 10C/50F 20C/68F 30C/86 40C/104F
3000 Distance 860ft 925ft 995ft 1070ft 1150ft
Density ALT 1904ft 3112ft 4268ft 5376ft 6440ft
Velocity 95fps 96fps 98fps 99fps 100fps
KTAS 56 57 58 59 60
Time 18sec 19sec 20sec 21sec 23sec
Thrust 532lbs 513lbs 493lbs 475lbs 442lbs
(Effective)
Thrust - Drag - Runway Friction
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Equal Scale: Interval Data (Higher Level Measurement).
The temperature scale has equal intervals (zero, 10, 20, 30, & 40 degrees celsius).
The graph above is for a constant pressure altitude of 3,000 feet. The independent variables are temperature.
When we say that 40 degrees celsius is 20 degrees more than than 20 degrees celsius, that does not mean takeoff distance has doubled. That does not mean density altitude has doubled. That does not mean velocity and true airspeed has doubled. It also does not mean the time to accelerate to liftoff velocity has doubled. Pilots encounter performance discrepancies in the mountainous west and Appalachian Mountains when they think cooler temperatures yield proportional performance gains. The graph above shows the relationship of temperature to effective thrust. This does not mean causation. The combination of air density, vehicle mass, and acceleration rate are the causes. Tables, charts, and graphs help us to identify environmental and technological processes. The effect of takeoff thrust (an input) has a direct effect on takeoff velocity and takeoff distance (outputs). Notice the downward trend associated with temperature rise. An amber color should be understood as an expression of "caution."
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