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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.

Thanks for reading. These articles are my perspectives and are not meant to represent any employers' opinions. Always operate your aircraft per applicable SOPs, Stan Mans, and AFMs. Please help me out and submit any corrections on the contact form.
Copyright 2024

  • Home
    • Stage Checks and Checkrides >
      • General
      • Privileges and Limitations
      • Airworthiness
    • Memory aids
    • The 5 Fundamentals of Weather
  • Aero
    • Demystifying the basic lift equation
    • Density for Dummies
    • Speeds and Weight
    • Vmca Factors
    • OEI: The Gravity Tax
  • IFR
    • Vertical speeds on non-standard gradients
    • Turning inbound from an Arc
    • Turning onto an Arc
    • Outbound Holding time Adjustments
    • 60:1 and Derivations
    • 172 Attitude Flying
    • How to Ace GA Chart Briefings
    • IFR Briefings in Jets
    • OEI Approaches
  • Stick & Rudder
    • The Energy Box
    • Mastering Slow Flight
    • Improving Your Landings
    • Pattern Extensions
    • VMC Demo
    • OEI Flow in the Seminole
  • Jets
    • Landing the E175
    • E175 Flare Geometry
  • Systems
    • Constant-Speed Props
  • Airport Reports
    • KSLC LDA35
    • Sea-Tac Airport
  • Blog
  • Contact