How to find the induced drag factor

[Tomdickjerry]

Homework Statement

An aircraft has a mass of 1100kg and a wingspan of b=9.75m. the surface of the wing is 15m2 and its span effciency factor e=0.90. the parasitic drag at zero lift of the aircraft CD0 is 0.0225. Take density of the air to be 1.225kg/m3

The aircraft has lost power and is gliding to the ground. Assume that the glide angle ϒ is small
Find the induced drag factor k.

Homework Equations

the only equation i can think of is
D=1/2pv2s(CD0+kCl2)

The Attempt at a Solution

Assuming almost level flight L=W=1100kg
unable to figure a way out to eliminate the velocity factor

Please help! Thanks!

 

[KataKoniK]

Hi there,

Thank you for your post. Let's start by defining some terms and variables:
- m = mass of the aircraft (1100 kg)
- b = wingspan (9.75 m)
- S = wing surface area (15 m^2)
- e = span efficiency factor (0.90)
- CD0 = parasitic drag at zero lift (0.0225)
- ρ = density of air (1.225 kg/m^3)
- v = velocity of aircraft
- L = lift
- D = drag
- k = induced drag factor

From the given information, we can use the following equations:
1. Lift equation: L = 1/2 * ρ * v^2 * S * Cl
2. Drag equation: D = 1/2 * ρ * v^2 * S * (CD0 + k * Cl^2)
3. Glide angle equation: tan(ϒ) = D/L

We know that the aircraft is gliding, so the lift and weight are equal (L = W). Therefore, we can substitute L with W in equation 3:
tan(ϒ) = D/W

We also know that the velocity is directly proportional to the lift and drag, so we can eliminate v by dividing equation 1 by equation 2:
L/D = Cl/(CD0 + k * Cl^2)

Substituting L/D with tan(ϒ), we get:
tan(ϒ) = Cl/(CD0 + k * Cl^2)

Now, we can rearrange the equation to solve for k:
k = (tan(ϒ) - CD0) / (Cl^2 / Cl)

Since the glide angle (ϒ) is small, we can approximate tan(ϒ) to ϒ. Also, the lift coefficient (Cl) can be approximated to the weight divided by the lift equation (W/ (1/2 * ρ * v^2 * S)):
Cl = 2 * W / (ρ * v^2 * S)

Substituting these approximations into the equation for k, we get:
k = (ϒ - CD0) / (2 * W / (ρ * v^2 * S)^2)

Finally, we can plug in all the given values and solve for k:
k = (ϒ - 0.0225) / (