P (power) must be in ft-#/sec (foot pounds of work per second) in order to produce R/C (rate of climb) in ft/sec. To express P in HP, convert HP to ft-# /minute. 1 HP = 550 ft-#/sec, or 60 (550) = 33,000 ft-#/min: Then R/C will be in ft/min Thus we may rewrite the equation as R/C = 33,000 (PA PR) / W where – P is in HP W is in # R/C is in ft/min For the equation R/C = V (TA TR) / W: – T and W are in #. If V is in KTAS, R/C will be in KTAS Convert V from nm/hr to ft/min: Then R/C will be in ft/min. Thus we may rewrite the equation as R/C = (6076/60) V (TA TR) / W – where T and W are in # (with TR = DT) V is in KTAS R/C is in ft/min Summary of Equations: Climb Angle R/C R/C = 33,000(PA PR) / W – c = sin-1 [(TA TR) / W] – R/C = (6076/60) V (TA TR) / W – TA, TR (DT), and W in #; V in KTAS; P in HP; R/C in fpm Example Calculations Corporate jet airplane at SL in SA (so EAS = TAS): 20,000# gross VY = 250 KEAS. TA = 5,000# thrust SL SA DT at VX = 3,700# VX = 165 KEAS DT at VY = 4,000#. Rate of climb and angle of climb at VY = 250 KTAS; TR = DT = 4000#: R/CMAX = (6076/60) V (TA - TR) / W = [(6076 / 60) 250 (5,000 4,000)] / 20,000 = 1,265.833334 fpm. –
P (power) must be in ft-#/sec (foot pounds of work per second) in order to produce R/C (rate of climb) in ft/sec. To express P in HP, convert HP to ft-# /minute. 1 HP = 550 ft-#/sec, or 60 (550) = 33,000 ft-#/min: Then R/C will be in ft/min Thus we may rewrite the equation as R/C = 33,000 (PA – PR) / W where P is in HP W is in # R/C is in ft/min For the equation R/C = V (TA – TR) / W: T and W are in #. If V is in KTAS, R/C will be in KTAS Convert V from nm/hr to ft/min: Then R/C will be in ft/min. Thus we may rewrite the equation as R/C = (6076/60) V (TA – TR) / W where T and W are in # (with TR = DT) V is in KTAS R/C is in ft/min Summary of Equations: Climb Angle R/C c = sin-1 [(TA – TR) / W] R/C = 33,000(PA – PR) / W R/C = (6076/60) V (TA – TR) / W TA, TR (DT), and W in #; V in KTAS; P in HP; R/C in fpm Example Calculations Corporate jet airplane at SL in SA (so EAS = TAS): 20,000# gross TA = 5,000# thrust SL SA VX = 165 KEAS VY = 250 KEAS. DT at VX = 3,700# DT at VY = 4,000#. Rate of climb and angle of climb at VY = 250 KTAS; TR = DT = 4000#: R/CMAX = (6076/60) V (TA - TR) / W = [(6076 / 60) 250 (5,000 – 4,000)] / 20,000 = 1,265.833334 fpm.