engineering

Sears–Haack body

Sears–Haack body is a engineering topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Sears–Haack body rather than just read about it. In short: The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a slender solid body of revolution with a given body length and volume. The mathematical derivation assumes small-disturbance (linearized) supersonic flow, which is governed by the Prandtl–Glauert equation.

Key takeaways

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

Reference excerpt

The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a slender solid body of revolution with a given body length and volume. The mathematical derivation assumes small-disturbance (linearized) supersonic flow, which is governed by the Prandtl–Glauert equation. The derivation and shape were published independently by two separate researchers: Wolfgang Haack in 1941 and later by William Sears in 1947. The Kármán–Moore theory indicates that the wave drag scales as the square of the second derivative of the area distribution, D wave ∼ [ S ″ ( x ) ] 2 {\displaystyle D_{\text{wave}}\sim \left[S''\left(x\right)\right]^{2}} (see full expression below), so for low wave drag it is necessary that S ( x ) {\displaystyle S(x)} be smooth. Thus, the Sears–Haack body is pointed at each end and grows smoothly to a maximum and then decreases smoothly toward the second point.

Useful formulas Because these formulas assume a slender body, they assume L >> 2Rmax (i.e. a large fineness ratio f = ⁠L/2Rmax⁠), but no specific upper limit on Rmax (or lower limit on fineness) is specified.

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Sears–Haack body

Start with the simplest possible case. Write down what Sears–Haack body claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In engineering, 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 Sears–Haack body 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 Sears–Haack body 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 Sears–Haack body

In research: Sears–Haack body appears in engineering 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 Sears–Haack body 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: Sears–Haack body is common in secondary-school and first-year university syllabi. It links to neighbouring topics Aerodynamics, so understanding it makes those chapters shorter.
In everyday life: Look for Sears–Haack body 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Sears–Haack body” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Sears–Haack body in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Sears–Haack body 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 Sears–Haack body out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Sears–Haack body in simple terms?

Why does Sears–Haack body matter?

Because it connects several engineering 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 Sears–Haack body?

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 Sears–Haack body.