## Speed and weight

Much is made about maneuvering speed and how it changes with the weight of the aircraft. You sometimes see questions on written tests about the fact that "there's no Va on the ASI because it's weight-dependent so it's not just one number." That same logic applies to many other speeds, but they don't seem to get as much attention. Let's delve into some of these and see how we can fly more intelligently.

As a review, lift is a function of a few variables. More here if you're not familiar with those yet.

L = ½ CL * S * ρ * α * v^2

We also know that in straight-and-level flight weight = lift, or W = L = ½ CL * S * ρ * α * v^2. If we assume that we're not changing flap settings (CL and S), ρ, or α, then we can hold those constant and say W = L = v^2. If we want to know what happens to speeds as we change weight from w (given weight) to W (baseline weight), we can model that as follows:

w/W = v^2/V^2

Taking the square root of both sides gives us

√(w/W) = v/V or √∆w = ∆v

In other words, speed changes as the square root of weight does. Let's look at some example of where this applies:

Maneuvering speed: speed at which the load factor exceeds a critical value before stalling.

Stall speed: like maneuvering speed, there is a speed where you max out α for a given lift. This will scale as √∆w.

Approach speed: if we need a given amount of lift or 1.3 Vso, that's likewise a √∆w relationship.

Application: let's say your small aircraft POH says you should fly a short-field landing at 61 KIAS at 2550 lbs. To figure out your approach speed at 2300 lbs, we plug that in to get

√w/W = √2300/2500 = .95 = v/V 58/61

If the book calls for 61 KIAS at 2550, try 58 KIAS at 2300 next time (apply whatever gust corrections as normal). I bet it'll be easier to avoid floating past your target.

As a review, lift is a function of a few variables. More here if you're not familiar with those yet.

L = ½ CL * S * ρ * α * v^2

We also know that in straight-and-level flight weight = lift, or W = L = ½ CL * S * ρ * α * v^2. If we assume that we're not changing flap settings (CL and S), ρ, or α, then we can hold those constant and say W = L = v^2. If we want to know what happens to speeds as we change weight from w (given weight) to W (baseline weight), we can model that as follows:

w/W = v^2/V^2

Taking the square root of both sides gives us

√(w/W) = v/V or √∆w = ∆v

In other words, speed changes as the square root of weight does. Let's look at some example of where this applies:

Maneuvering speed: speed at which the load factor exceeds a critical value before stalling.

Stall speed: like maneuvering speed, there is a speed where you max out α for a given lift. This will scale as √∆w.

Approach speed: if we need a given amount of lift or 1.3 Vso, that's likewise a √∆w relationship.

Application: let's say your small aircraft POH says you should fly a short-field landing at 61 KIAS at 2550 lbs. To figure out your approach speed at 2300 lbs, we plug that in to get

√w/W = √2300/2500 = .95 = v/V 58/61

If the book calls for 61 KIAS at 2550, try 58 KIAS at 2300 next time (apply whatever gust corrections as normal). I bet it'll be easier to avoid floating past your target.