There is no point reaching for a calculator that cannot show its working. This one starts from true airspeed (v), friction coefficient (μ), custom value of μ, g, maximum or minimum speed?, turn radius (r), turn radius (r), banking angle (θ), banking angle (θ), angle of banking (θ), tan and atan and reports angle of banking (θ), speed (v) and radius of the turn (r), so you can see how each answer follows from the numbers you entered.
What Is the Bank Angle Calculator?
This bank angle calculator is for the kind of problem where you know the physical quantities but not the number you need. It turns true airspeed (v), friction coefficient (μ), custom value of μ, g, maximum or minimum speed?, turn radius (r), turn radius (r), banking angle (θ), banking angle (θ), angle of banking (θ), tan and atan into angle of banking (θ), speed (v) and radius of the turn (r).
Physics calculations go wrong in predictable ways, usually through mixing units or dropping a digit. Work through the result one step at a time and check that the figures are the size you would expect at each stage.
How the Bank Angle Physics Works
The relationship is applied step by step, and each step is a standard piece of physics rather than a single opaque formula. That means you can check the intermediate values against what the theory predicts, which is usually faster than checking only the final answer.
Keep every value in the same unit system throughout the calculation. Mixing metres and feet part way through is the single most common reason a correct formula gives a wrong answer.
Units, Assumptions and the Limits of the Model
The calculation assumes ideal conditions: no air resistance, no heat loss, and dimensions that do not change while you work. Those assumptions are reasonable for most classroom and engineering estimates, and unreasonable for anything more precise.
Where a value is a rate, it has to be quoted for the same period as everything else. A per-hour figure cannot be combined with a per-day figure without converting one of them first.
A Worked Example
Working through an example, with true airspeed (v) set to 10, friction coefficient (μ) set to 0.7, custom value of μ set to 5, the calculator returns speed (v) of -, and speed (v) (speed custom) of 2.17279, and angle of banking (θ) of -. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out angle of banking (θ)?
Enter true airspeed (v), friction coefficient (μ), custom value of μ, g, maximum or minimum speed?, turn radius (r), turn radius (r), banking angle (θ), banking angle (θ), angle of banking (θ), tan and atan. The calculator then works through the relationship and reports angle of banking (θ), speed (v) and radius of the turn (r).
What does the bank angle actually calculate?
It takes true airspeed (v), friction coefficient (μ), custom value of μ, g, maximum or minimum speed?, turn radius (r), turn radius (r), banking angle (θ), banking angle (θ), angle of banking (θ), tan and atan and converts them into angle of banking (θ), speed (v) and radius of the turn (r) using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter true airspeed (v)?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Is the answer exact?
It is as exact as the formula and the inputs allow. The method itself is the standard one for this problem, so the only sources of error are the figures you enter and the precision you ask for.
Can I use this for a quick estimate as well as a precise answer?
Yes. The calculator is built for quick checks, so round your inputs to a sensible number of significant figures and the result will be just as useful. If you need more precision, keep the same method and add digits to the inputs rather than adjusting the method itself.