Lock number

Key takeaways

Lock number belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Lock number to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Lock number from memory before moving on to harder problems.

Reference excerpt

In helicopter aerodynamics, the Lock number is the ratio of aerodynamic forces, which act to lift the rotor blades, to inertial forces, which act to maintain the blades in the plane of rotation. It is named after C. N. H. Lock, a British aerodynamicist who studied autogyros in the 1920s. Typical rotorcraft blades have a Lock number between 3 and 12, usually approximately 8. The Lock number is typically 8 to 10 for articulated rotors and 5 to 7 for hingeless rotors. High-stiffness blades may have a Lock number up to 14. Larger blades have a higher mass and more inertia, so tend to have a lower Lock number. Helicopter rotors with more than two blades can have lighter blades, so tend to have a higher Lock number. A low Lock number gives good autorotation characteristics due to higher inertia, however this comes with a mass penalty. Ray Prouty writes, "The previously discussed numbers: Mach, Reynolds and Froude are used in many fields of fluid dynamic studies. The Lock number is ours alone."

Definitions For a rectangular blade of radius R {\displaystyle R} , and chord c {\displaystyle c} , the Lock number γ {\displaystyle \gamma } , is calculated as,

γ = ρ C L α c R 4 I b {\displaystyle \gamma ={\frac {\rho C_{L\alpha }cR^{4}}{I_{b}}}}

where:

ρ {\displaystyle \rho } is the density of air

C L α = ∂ C L ∂ α {\displaystyle C_{L\alpha }={\frac {\partial C_{L}}{\partial \alpha }}} is the lift-curve slope of the airfoil

I b {\displaystyle I_{b}} is the blade mass moment of inertia about the flapping axis.

See also Coning Mach number Froude number Reynolds number

References

Worked examples

Example 1 — a first encounter with Lock number

Start with the simplest possible case. Write down what Lock number claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Lock number before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Lock number ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Lock number

In research: Lock number appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Lock number in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Lock number is common in secondary-school and first-year university syllabi. It links to neighbouring topics Aviation stubs, Engineering ratios, Fluid dynamics stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Lock number outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Lock number in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Lock number means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Lock number out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Lock number in simple terms?

In helicopter aerodynamics, the Lock number is the ratio of aerodynamic forces, which act to lift the rotor blades, to inertial forces, which act to maintain the blades in the plane of rotation. It is named after C.

Why does Lock number matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Lock number?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Lock number.