(Solved): answers are provided at the bottom Maximum available shaft power should be assumed to decrease in p ...
answers are provided at the bottom
Maximum available shaft power should be assumed to decrease in proportion to relative dens 1 Use the data in Table 1 to calculate the following: (a) Vmd,Vmp and Pmin (b) Shaft power output required to achieve (i) Straight-and-level flight at 160ms−1, (ii) Best rate of climb of 10ms−1. (iii) Correctly banked turn, normal load factor 2.5 , at a speed of 100ms−1. In each case, give the associated values of CL and CD. (c) Ambient density at absolute ceiling altitude, based on an installed power (quoted at ISA sea level) of 8MW. (d) Gross still-air range and endurance at constant altitude of 25,000ft ( ρ/ρst=0.45) and constant true air speed of 120m/s. The initial mass is 35000kg of which 10000kg is cruise fuel. Q1 (a) Vmd=81.3m/sVmp=61.8m/sPmin=1385.1kW (a) (CLmd=0.71CLmp=1.22) (b)(i) Straight \& Level fight V=160.00m/s: Pshaft=7555.4kW (CL=0.182 CD=0.021) (b)(ii) For 10.00m/s best rate of climb: Pshaft=5668.9kW (b)(iii) n=2.5 Tum @ V=100.0m/s: Pshaft =6446.9kW (c) relative density at celling altitude =0.346,Vmp=105.0m/s (d) Gross Stir-Air Range R=5074.3km@V=120.0m/s, sigma=0.45 Duration =11.75 hours
To solve the given questions, we'll need to apply various formulas and calculations using the provided data. Let's go through each question step by step.(a) Vmd, Vmp, and Pin:Vmd (Design dive speed) can be calculated using the formula:Where:
Mass = 35,000 kg (given)
g = Acceleration due to gravity = 9.81 m/s²
? = Air density
S = Wing reference area = 120 m² (given)
C = Maximum lift coefficient = 2.0 (given)To find Vmd, we need to know the value of ? (air density). Since it's not given, we'll assume it to be the standard sea-level density at ISA conditions, which is approximately 1.225 kg/m³.Vmd =
=
= 48.3 m/sVmd (Design dive speed) is approximately 48.3 m/s.Vmp (Max speed in level flight) can be calculated using the formula:Vmp = Where:
C = Maximum lift coefficient = 2.0 (given)
Co = Drag polar = 0.02 + 0.04 * CCo at C = 2.0:
Co = = 0.02 + 0.08
= 0.10Vmp =
=
? 216 m/sVmp (Max speed in level flight) is approximately 216 m/s.Pin (Installed power required) can be calculated using the formula:Pin = Where:
? = Propeller efficiency = 85% = 0.85 (given)Pin =
? 97434 WPin (Installed power required) is approximately 97434 W.