Aerodynamics Find max forward airspeed & best glide speed

Unaccelerated Performance Rate Of Climb (ROC) = Vk LaTeX: \ast\sin\gamma ∗ sin ⁡ γ ∗ sin ⁡ γ = Vk LaTeX: \frac{Ta-Tr}{W} T a − T r W T a − T r W Variables needed are (Ta) and (Tr) and Velocity (V). Rate of Climb = available power (Ta) - required power (Tr) Max rate of climb = when the available power and required power is at its largest difference Tr is a constant 250 at lbs, largest thrust available difference would require 100% rpm range. Ta roughly 700lbs at 100% rpm. ROC= Vk LaTeX: \frac{Ta-Tr}{W} T a − T r W T a − T r W (1 knot = 101.3 fpm) V= LaTeX: \sqrt{\frac{W}{\frac{1}{2}\rho\ast\:S\ast C_L}} W 1 2 ρ ∗ S ∗ C L LaTeX: \sqrt{\frac{2500}{\frac{1}{2}\ast.0014\ast181\ast1.137}} 2500 1 2 ∗ .0014 ∗ 181 ∗ 1.137 = 131.735 knots Vk LaTeX: \frac{Ta-Tr}{W} T a − T r W LaTeX: \left(101.3\right)\ast131.735\ast\frac{700-250}{2500} ( 101.3 ) ∗ 131.735 ∗ 700 − 250 2500 = 2402.06 fpm Ta was estimated off of engine horsepower and Tr was based off of an approximation of 1/10 of the aircraft weight. Bringing Ta to 700 and Tr to 250. Once those values were known then the difference between the two are divided by the aircraft weight and multiplied by the fpm conversion and velocity (V) which was solved for above. Best Angle of Climb T= LaTeX: \frac{325\left(Horsepower\right)}{V_k} 325 ( H o r s e p o w e r ) V k = 740.122 LaTeX: \sin\gamma\:=\:\frac{T-D}{W} sin ⁡ γ = T − D W LaTeX: \frac{740.122-203}{2500} 740.122 − 203 2500 = .215 arcsin (.215)= 12.42 degrees The horsepower of this aircraft's engine is 300. So 300 multiplied by 325 and divided by our previous Vk (101.375). To get the proper angle we also needed the total drag from our previous assignment. Dt was 203. Maximum Range Airspeed The maximum endurance is simply the point where stable flight is achievable and the LaTeX: \frac{C_L\:^{\frac{3}{2}}}{C_D} C L 3 2 C D is at it's highest. We need to first look at the table. The airfoil is most efficient at 60 knots; however, 60 kts is below the stall speed for the aircraft. Let's pick the next highest VKTAS beyond the stall speed. VS=76.7 kts. The next higher airspeed in the table is 80 kts. Simply plug the numbers into the given formula. 80 kts = LaTeX: \frac{C_L^{\frac{3}{2}}}{C_D}\:\:\:\:\:\:\:\:\:\:\frac{0.639^{\frac{3}{2}}}{0.02020573}=25.28 C L 3 2 C D 0.639 3 2 0.02020573 = 25.28 We are told to look for where this number is the highest. We could either look at the graph, or run some more calculations. 100 kts = LaTeX: \frac{0.409^{\frac{3}{2}}}{0.01984373}=13.18 0.409 3 2 0.01984373 = 13.18 120 kts = LaTeX: \frac{0.284^{\frac{3}{2}}}{0.01964699}=7.7 0.284 3 2 0.01964699 = 7.7 140 kts = LaTeX: \frac{0.209^{\frac{3}{2}}}{0.01952894}=4.89 0.209 3 2 0.01952894 = 4.89 Notice the trend of decreasing numbers as velocity increases. This means that we need to stay as close to stall speed as possible while staying above it. According to the table, 80 kts is the most effective airspeed. Find maximum forward speed & best glide speed??