Calculate the ratio of the drag force on a passenger jet flying with a speed of 850 km/h at an altitude of 10 km to the drag force on a prop-driven transport flying at three-fifths the speed and half the altitude of the jet. At 10 km the density of air is 0.38 kg/m3 and at 5.0 km it is 0.67 kg/m3. Assume that the airplanes have the same effective cross-sectional area and the same drag coefficient C.
(drag on jet / drag on transport) =
Surely you have an equation for drag force as a function of density, C, and speed.
I have D=.5CpAv^2, do i just ignore C and A?? not quite sure what to do...
Okay i figured it out. thanks for your assistance I wasn't looking in the right place
To calculate the ratio of the drag force on the jet to the drag force on the prop-driven transport aircraft, we will use the formula:
Drag force = 0.5 * density * (speed^2) * C * A
Where:
- density is the air density
- speed is the velocity of the aircraft
- C is the drag coefficient
- A is the cross-sectional area
First, let's calculate the drag force on the jet:
1. Density at 10 km altitude is given as 0.38 kg/m^3.
2. The speed of the jet is given as 850 km/h. Convert it to m/s: 850 km/h * (1000 m/km) / (3600 s/h) = 236.11 m/s.
3. The altitude of the jet is given as 10 km.
4. The density and altitude data given for the transport aircraft are irrelevant to the jet, so we won't use them for this calculation.
5. We assume that the jet and transport aircraft have the same effective cross-sectional area (A) and drag coefficient (C).
Now, we can calculate the drag force on the jet:
Drag force on the jet = 0.5 * 0.38 kg/m^3 * (236.11 m/s)^2 * C * A
Next, let's calculate the drag force on the transport aircraft:
1. The speed of the transport aircraft is given as three-fifths (3/5) of the jet's speed. Calculate it: 236.11 m/s * (3/5) = 141.67 m/s.
2. The altitude of the transport aircraft is given as half (1/2) of the jet's altitude. Calculate it: 10 km * (1/2) = 5 km.
3. The density at 5 km altitude is given as 0.67 kg/m^3.
4. Like before, we assume that the jet and transport aircraft have the same effective cross-sectional area (A) and drag coefficient (C).
Now, we can calculate the drag force on the transport aircraft:
Drag force on the transport aircraft = 0.5 * 0.67 kg/m^3 * (141.67 m/s)^2 * C * A
Finally, we can calculate the ratio of the drag force on the jet to the drag force on the transport aircraft:
(drag on jet / drag on transport) = (0.5 * 0.38 * (236.11)^2 * C * A) / (0.5 * 0.67 * (141.67)^2 * C * A)
Simplifying the equation, we can cancel out C and A:
(drag on jet / drag on transport) = (0.38 * (236.11)^2) / (0.67 * (141.67)^2)