Advance ratio and wingtip ratio

Theory and Concepts
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What are the best values for advance ratio of a propeller and wingtip ratio for a tubrine. Are they the same

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This text is generated by AI trained by Professor Kirby on his lectures, videos, notes, message board responses, and textbook

PK Bot’s answer:
Below is an explanation of the two ratios and clarification regarding whether they are “the same”:

  • The advance ratio for a propeller is defined roughly as the ratio of the free‐stream speed to the tip speed of the propeller blades. In our course material, it is given (up to a constant factor) as

    \text{advance ratio} \sim \frac{U_\infty}{\omega R},

    where
    • U_\infty is the free-stream (or vehicle) speed,
    • \omega is the propeller’s rotation rate (in radians per unit time), and
    • R is the propeller radius.

    In practice, definitions vary. usually “advance ratio” compares U_\infty to \omega R, whereas “advance coefficient” compares U_\infty to nD. \omega is angular velocity in rad/s which is 2\pi higher than n which is revolution rate in revs/s. D is diameter which is 2 times higher than R which is the radius. But the words are not always used consistently and YMMV.

  • The term tip‑speed ratio (which you referred to as “wingtip ratio for a tubrine”) is used in the context of wind turbines. It is defined as

    \text{tip-speed ratio} \equiv \lambda = \frac{\omega R}{U_\infty}.

    The tip-speed ratio has a clear definition and there are not random factors of 2 or 2\pi that vary depending on who is talking. Notice that the tip-speed ratio is essentially the inverse of the advance ratio, with perhaps differences in 2 or 2\pi or \pi depending on the definition

For most modern wind turbines, the optimum tip-speed ratio is about 6\pi/s, where s is the number of blades in the rotor. That maximizes extraction efficiency, which is the relevant figure of merit for a wind turbine.

For a propeller, the relevant figure of merit is different, so the best value actually isn’t the inverse of the value for the wind turbine. Wind turbine efficiency is defined as a measure of how much energy is extracted from the fluid compared to comparable wind turbines of the same radius in the same windspeed. Propeller efficiency is a measure of the power added to the vehicle, not the power added to the fluid. So if the propeller isn’t moving, its efficiency is zero. This tends to make propeller efficiency peak at higher values of J than you would expect from taking the inverse of \lambda.

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In summary, although they are closely related (indeed, they are inverses of one another, up to a constant if one uses an “advance coefficient”), the optimum value of the advance ratio for a propeller and the optimum tip‑speed ratio for a wind turbine are not the same. They serve different design purposes:

• For a propeller, the advance ratio indicates how fast the vehicle is moving relative to the blade tip speed and is chosen to optimize the thrust produced for a given power input.
• For a wind turbine, the tip‑speed ratio is chosen to maximize the aerodynamic power capture from the wind.

In crafting this response, I dedicated some time to reviewing the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I found these sections to be particularly helpful in formulating my answer. I encourage you to explore the pertinent ones directly:

Textbook sections:

  1. Chapter 2 How Stuff Works: How a propeller works (RELEVANT)
  2. Chapter 7.1: Helicopter/Quadcopter Rotors (MARGINALLY RELEVANT)
  3. Chapter 9 How Stuff Works: How winglets work (MARGINALLY RELEVANT)
  4. Chapter 9.2: Engineering Descriptions of Airfoil Forces (MARGINALLY RELEVANT)
  5. Chapter 2 How Stuff Works: How a wind turbine works (MARGINALLY RELEVANT)
  6. Chapter 9.1: How Airfoils Work (MARGINALLY RELEVANT)
  7. Chapter 9 Fundamentals: Derivation of Thin Airfoil Theory (MARGINALLY RELEVANT)
  8. Chapter 9 How Stuff Works: Wind turbine design step 2: blade design (MARGINALLY RELEVANT)
  9. Chapter 9.7: Models (MARGINALLY RELEVANT)
  10. Chapter 9 How Stuff Works: Wind turbine design step 1: rotor disk analysis (MARGINALLY RELEVANT)

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