physics

Von Kármán–Gabrielli diagram

Von Kármán–Gabrielli diagram is a physics 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 Von Kármán–Gabrielli diagram rather than just read about it. In short: The von Kármán–Gabrielli diagram (also Gabrielli–von Kármán diagram, GvK diagram) is a diagram which compares the efficiency of transportation methods by plotting specific tractive force, or specific resistance (ε = P/mgv = E/mgL) against velocity (v). It first appeared in Theodore von Kármán's ASME Thurston Lecture, and in the 1950 paper on this subject by Giuseppe Gabrielli and von Kármán.

Key takeaways

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

Reference excerpt

The von Kármán–Gabrielli diagram (also Gabrielli–von Kármán diagram, GvK diagram) is a diagram which compares the efficiency of transportation methods by plotting specific tractive force, or specific resistance (ε = P/mgv = E/mgL) against velocity (v). It first appeared in Theodore von Kármán's ASME Thurston Lecture, and in the 1950 paper on this subject by Giuseppe Gabrielli and von Kármán.

Details In GvK diagram, the x-axis is the vehicle velocity, and the y-axis is the dimensionless specific resistance. The same kind of vehicle may have multiple different operating velocities, with different corresponding specific resistances, consequently each kind of vehicle generally correspond to a whole region on the GvK diagram, but only the lower-edge of the region is plotted, since specific resistance can always be artificially increased by wasting energy, but not decreased beyond a lower limit depending on the physical and engineering constraints. The specific resistance is a dimensionless quantity defined by ϵ := P / m g v {\displaystyle \epsilon :=P/mgv} where P {\displaystyle P} is the total power consumption by the vehicle, m {\displaystyle m} is the total mass of the vehicle, g {\displaystyle g} is the gravitational constant, and v {\displaystyle v} is the velocity of the vehicle. The inverse of specific resistance is defined as transport efficiency.

Alternative forms of specific resistance For example, if we have a freight vehicle in which most of the total mass is in its freight, and we have freight to carry over a distance of L {\displaystyle L} , but we have no requirement for how long it should take, then the total energy consumption of the vehicle over the journey is E = P t = P ( L / v ) = ϵ ( m g L ) {\displaystyle E=Pt=P(L/v)=\epsilon (mgL)} so we can interpret the specific resistance as a ratio for how much resistance the vehicle faces. A low resistance means it needs to consume less energy to carry the same load through the same distance. The power is equal to the drag force times velocity. For aircraft in cruise flight the lift is equal to the weight (L=mg) and the engine thrust is equal to the drag (T=D). Hence, ϵ = P / ( m g v ) = D / L = 1 / f {\displaystyle \epsilon =P/(mgv)=D/L=1/f} with f = L / D {\displaystyle f=L/D} the lift-to-drag ratio, so the specific resistance of airplanes is roughly equal to the inverse of the lift-to-drag ratio.

The limit line The original paper by Gabrielli and von Kármán already noted that for all single vehicles they studied, there is a limit of the form ϵ ≥ A v {\displaystyle \epsilon \geq Av} , for some constant A ≈ 0.00175 m p h − 1 = 4 ×

10 − 4 s / m {\displaystyle A\approx 0.00175\;\mathrm {mph} ^{-1}=4\times {}10^{-4}\mathrm {s/m} } , which exhibits itself as a straight line on Figure 3. The constant A {\displaystyle A} can be interpreted as a measure of inefficiency. For vehicles in a convoy, such as a long train or a group of cars moving in a long tandem, the constant can be improved, decreasing energy dissipation to air resistance. Figure 5 shows a 4-fold improvement. Technological improvements over the years can move the limit line downwards. For example in 1980, the ultra large crude carrier (ULCC) could reach a limit of 3.6 ×

10 − 4 s / m {\displaystyle 3.6\times {}10^{-4}\mathrm {s/m} } . A report in 2004 demonstrated further improvements. For vehicles moving through fluid (ships, submarines, planes, etc), the specific energy is a dimensionless quantity defined as the Froude number divided by the specific resistance: ϵ E = F r / ϵ {\displaystyle \epsilon _{E}=\mathrm {Fr} /\epsilon } . A 1980 report showed that the specific energy has an upper limit of 200 over all kinds of vehicles moving through fluid, except rocket-powered vehicles (missiles, space rockets, etc) which can reach over 3000 specific energy.

The triangular gap If land vehicles are excluded from the GvK diagram, then a large triangular "gap" appears, spanned by merchant ship, destroyer, and commercial airplane, with airship being the lone inhabitant of the gap. After the GvK diagram became more widely known to marine engineers, a large number of designs were promoted to fill the gap, such as planing boats, hydrofoils, hovercraft and ground-effect vehicles, without success.

Numerical examples According to calculations done by Qian Xuesen, a rocket with an average speed of 2 km/s over a 5000 km range would require a thrust of 845,000 N for 140 seconds, with initial mass 44,000 kg and final mass 8,600 kg. This corresponds to ϵ ≈ 0.2 , A ≈ 1.0 ×

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Von Kármán–Gabrielli diagram

Start with the simplest possible case. Write down what Von Kármán–Gabrielli diagram claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, 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 Von Kármán–Gabrielli diagram 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 Von Kármán–Gabrielli diagram 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 Von Kármán–Gabrielli diagram

In research: Von Kármán–Gabrielli diagram appears in physics 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 Von Kármán–Gabrielli diagram 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: Von Kármán–Gabrielli diagram is common in secondary-school and first-year university syllabi. It links to neighbouring topics Diagrams, Energy in transport, so understanding it makes those chapters shorter.
In everyday life: Look for Von Kármán–Gabrielli diagram 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 “Von Kármán–Gabrielli diagram” →

Affiliate

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

How to study Von Kármán–Gabrielli diagram in 20 minutes

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

Frequently asked questions

What is Von Kármán–Gabrielli diagram in simple terms?

Why does Von Kármán–Gabrielli diagram matter?

Because it connects several physics 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 Von Kármán–Gabrielli diagram?

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 Von Kármán–Gabrielli diagram.