Question

Calculate the induced drag of the SR-71 Blackbird aircraft. Let the span efficiency factor, e=0.6. Assume that the weight of the vehicle is 637,650 N. The vehicle is flying at M[infinity] =3 in straight and levelflight at an altitude where the ambient pressure P[infinity] =1185 N/m² and the ambient temperature T[infinity] =231.2 K (recall R=287 J/kg−K for air). Planform area of the vehicle is 170 m² and AR=1.7. For your calculations, assume that the entire vehicle may be treated as a 'finite' flying wing with parameters as given.

Answer 1

The induced drag of the SR-71 Blackbird can be calculated using known parameters and the formula for induced drag. It requires the computation of air density, which is calculated from pressure and temperature, and the true airspeed based on the Mach number and conditions provided.

Step-by-step explanation:

The induced drag of an aircraft can be calculated using the induced drag equation: Di = (2 * L2) / (ρ * V2 * A * π * AR * e). In this equation, Di is the induced drag, L is the lift force which equals the aircraft's weight in straight and level flight, ρ is the density of air, V is the velocity, A is the planform area, AR is the aspect ratio, and e is the span efficiency factor.

Given data for the SR-71 Blackbird aircraft:

• Weight (W) = 637,650 N
• Span efficiency factor (e) = 0.6
• Ambient pressure (P∞) = 1185 N/m²
• Ambient temperature (T∞) = 231.2 K
• Planform area (A) = 170 m²
• Aspect ratio (AR) = 1.7
• Mach number (M∞) = 3
• The specific gas constant for air (R) = 287 J/kg∗K

To find the density of air, we use the equation ρ = P / (R * T). Once the density is calculated, we can find the true airspeed using the Mach number and the speed of sound equation. With all these values, we can calculate the induced drag.

It's important to note that aerodynamics plays a significant role in vehicle design, as drag forces significantly impact fuel efficiency, as seen in automobiles' performance at highway speeds.