The Jet Built to Leak
Picture a jet parked on a runway, dripping fuel from seams all along its belly. Puddles spread on the concrete. The ground crew isn't worried, because the jet was built to leak.
The jet is the SR-71 Blackbird, a spy plane that first flew in 1964. In 1976 a Blackbird flew at 3,530 km/h (2,193 mph), about three times the speed of sound, and no jet-powered plane with a crew on board has officially flown faster since.
Make your guess. Why would engineers build a plane that leaks fuel on the ground?
- A leak-proof fuel tank was too heavy for a plane that fast
- The skin panels were fitted loosely, to leave room to grow when the plane got hot
- The dripping fuel kept the tires cool before takeoff
Show answer
B. The skin panels were fitted loosely, to leave room to grow when the plane got hot
The panels were fitted loosely on purpose. At three times the speed of sound, the skin got hotter than most kitchen ovens go, and hot metal grows. Loose on the ground, the panels pressed together only once the plane was hot, and the leaks slowed to almost nothing.
Start where the leaks stop. How fast does the Blackbird have to fly before the drips end?
Seal the leaks
Your goal: drag the speed from the runway to cruise, and watch the gaps between the skin panels.
The gaps close only near top speed, at about Mach 3.1. Below that speed, the Blackbird drips.
Did you see the drips get worse just after takeoff? Around 10 km up, the air is about −50 °C, so the skin gets colder than on the runway. Only at high speed does the skin heat up. But why does flying fast heat a plane at all?
Why fast air gets hot
Most people would guess rubbing, the way your hands warm up when you rub them together. Rubbing helps, but the bigger effect is squeezing. At Mach 3, the plane hits the air far faster than the air can get out of the way, so the air piles up in front of every edge and gets squeezed.
An animation of air meeting the Blackbird's pointed nose, seen from the plane. Far ahead, the bits of air are spread out and grey. At the nose, the bits crowd together into a thin layer along the skin and turn orange and red as the squeezed air heats up. The animation plays by itself in a loop. Every few seconds the motion slows almost to a stop, so you can see the crowd of hot air at the nose.
Text version
Seen from the plane, the air rushes toward the nose at Mach 3. Far ahead, the bits of air sit in even rows, spread out and cool. The air cannot get out of the way in time, so right at the nose each row is suddenly pushed close to the skin. The bits crowd into a thin layer that slides along both sides of the nose, and their colour changes from grey to orange and red, because squeezed air heats up.
Squeezed air heats up for the same reason a bike pump gets warm when you pump hard. The plane does work on the air, and that work becomes heat. So how much heat does a little more speed buy?
Suppose the Blackbird flies twice as fast. How much more does the squeezed air heat up?
- Twice as much
- Four times as much
- The same: air can only get so hot
Show answer
B. Four times as much
Four times as much. The heat comes from the air's energy of motion, and energy of motion grows with the speed squared. Twice the speed means four times the energy, and four times the heating.
Here is the line of math. Stop a kilogram of air that was rushing past at speed \(v\), and the air's energy of motion turns into heat. The air warms by:
Here \(c_p\) is about 1,000 joules per kilogram per degree: the energy that warms a kilogram of air by 1 °C. At Mach 3.2, \(v\) is about 944 m/s, and \(\Delta T\) comes out near 440 °C. An airliner at about 250 m/s warms the air by only about 30 °C.
The real skin ran cooler than 440 °C: roughly 240 to 330 °C on average, and over 500 °C near the engines. The air touching the skin is never stopped completely, and the paint helped too.
The first prototype flew in bare metal. A black surface gives off heat faster than a shiny one, so in late 1963 the engineers painted the whole fleet black, which gave the plane its nickname. What does that much heat do to metal?
Metal that grows
Heat a metal bar, and the bar gets longer. Hot atoms jiggle harder and shove their neighbours a little farther away, so the whole bar stretches. The stretch is called thermal expansion.
The stretch is tiny for each degree, but the Blackbird heated up by about 300 °C. The rule for how much a length \(L\) grows is:
The number \(\alpha\) depends on the metal. For titanium, \(\alpha\) is about 9 millionths per degree. Take the whole 33-metre plane and heat it by 280 °C, and the formula gives about 8 cm. Sources agree on "several inches": the Blackbird grew in flight.
So the designers made room for growth everywhere. The fuselage panels fit loosely on the ground, and the fuel tanks' sealant, which had to cope with −50 °C to over 300 °C, leaked until the skin warmed up. The wing skin was even rippled on purpose:
An animation of two strips of metal skin, each held between two fixed posts, heating up and cooling down. The flat strip bows out when hot. The rippled strip keeps its shape. The animation plays by itself in a loop. A bar at the top shows the heat. The strips hold still for a moment while they are hot, so you can compare them.
Text version
Two strips of metal skin are each held between two posts that cannot move. As the strips heat up, both get longer. The flat strip has nowhere to go, so it bows out into a hump, well away from its starting line. The rippled strip takes up the extra length in slightly deeper ripples and stays in a straight line between its posts. As the strips cool, the flat strip flattens again. This is why the Blackbird's wing skin was rippled on purpose.
The hot top of the plane even grew more than the fuel-cooled bottom, so the nose drooped at speed. Which metal can grow like that and stay strong?
Pick the metal
You are building the Blackbird's skin. It must stay strong at 300 °C and be light enough to fly. Which metal do you pick?
- Aluminium, like an airliner
- Steel
- Titanium
Show answer
C. Titanium
Titanium. Aluminium gets soft well below 300 °C, so the engineers ruled it out. Steel stays strong but is heavy. Titanium stays strong when hot and weighs a little over half as much as steel. The titanium alloy the Blackbird used was nearly twice as strong as stainless steel for its weight.
| Metal | At 300 °C | Weight |
|---|---|---|
| Aluminium | Goes soft | Lightest |
| Steel | Stays strong | Heaviest |
| Titanium | Stays strong | In between |
Titanium also grows less: about 0.9 mm per metre for every 100 °C, against about 1.2 to 1.7 mm for steel and 2.3 mm for aluminium. Between 85 and 93 percent of the Blackbird's structure was titanium, depending on how you count. Nobody had built a plane mostly from titanium before. "Everything had to be invented. Everything," the designer Kelly Johnson recalled.
Titanium fought back. Cadmium-plated tools made the metal brittle, and early drill bits wore out after 17 holes. Much of the raw titanium came from the Soviet Union, bought through middleman companies, according to accounts made public since.
The metal could take the heat. But the fuel sat in tanks right behind that 300 °C skin. Wouldn't the fuel catch fire?
Fuel that won't light
The Blackbird burned a special fuel, called JP-7, made to give off very little vapour. Ordinary jet fuel next to a 300 °C skin would be a risk. JP-7 is so hard to light that a lit match dropped into a puddle of JP-7 goes out.
So how do you start an engine on fuel that won't light? With a squirt of a chemical called triethylborane, or TEB, which bursts into flame the moment it touches air, with a green flash. And before the engines burned the fuel, the fuel had one more job:
Fuel was also the reason for the Blackbird's most famous habit: meeting a tanker plane for more fuel soon after takeoff. Why did the Blackbird refuel so early?
The tanker myth
Why did the Blackbird often take on fuel from a tanker soon after takeoff?
- The plane had leaked most of its fuel on the runway
- The plane took off with partly empty tanks on purpose
- JP-7 could only be pumped in while flying
Show answer
B. The plane took off with partly empty tanks on purpose
The plane took off with partly empty tanks on purpose. A lighter plane is easier on the brakes and tires, and a lighter plane can still get off the ground if one engine fails during takeoff. The tanker then filled the tanks in the air.
The leak story is the famous one, but histories of the Blackbird call the story a misconception: the leaks never cost enough fuel to force a refill. Fuel made up more than half of the plane's 63,000 kg takeoff weight, so leaving some behind made a big difference.
A full load of hot, non-flammable fuel still needs an engine that can eat air arriving at three times the speed of sound. How does an engine do that?
The moving spike
The spinning blades inside a jet engine can't handle air coming in faster than sound. So the Blackbird had to slow the air down before the engine got it. The job fell to the cone in front of each engine, called the spike.
A shock wave is a sudden step where fast air slows down and squeezes together. The spike makes a slanted shock wave at its tip. A last, straight-across shock wave sits just behind the narrowest point, and behind that shock the air is slow enough for the engine.
The faster the plane flies, the narrower that narrowest point has to be. The spike is fat in the middle, so sliding the spike back squeezes the gap: from Mach 1.6 to Mach 3.2 the spike slid back about 66 cm (26 inches).
Your goal: press Faster, then slide the spike back until the shock wave is in place. Reach Mach 3.2 without an unstart.
Slide the spike too far back, and the gap gets too narrow for all the air. The inlet throws the shock wave out the front, which is called an unstart. One engine suddenly loses push while the other keeps pushing, so the plane lurches sideways, hard. Crews have described their helmets slamming against the canopy. In the real plane, a computer moved the spikes.
Get the spike right, and something surprising happens. At Mach 3, the engine itself made only about 17 percent of the push. The squeezed air in the inlet made 54 percent, and the exhaust nozzle 29 percent. At cruise, the Blackbird was mostly pushed by its own air intake.
How it really works
That is the whole story in plain words. For the details, open the toggle.
How it really works (the physics, step by step)
- Squeezed air heats up. A kilogram of air rushing past at speed \(v\) carries \(\tfrac12 v^2\) joules of energy of motion. Bring the air to a stop against the plane, and that energy becomes heat. Warming the air by \(\Delta T\) at steady pressure takes \(c_p\,\Delta T\) joules, so
\[ c_p\,\Delta T = \tfrac12 v^2 \quad\Rightarrow\quad \Delta T = \frac{v^2}{2c_p} \]
- The numbers. With \(v = 944\) m/s and \(c_p \approx 1005\) J/(kg·°C):
\[ \Delta T = \frac{944^2}{2 \times 1005} \approx 443\ ^\circ\text{C} \]Air at about \(-56\) °C would reach about 390 °C if stopped completely.
- The same rule with the Mach number. Dividing by the air's own temperature \(T\) gives \(T_0 = T\left(1 + \tfrac{\gamma - 1}{2} M^2\right)\) with \(\gamma = 1.4\) for air, so \(T_0 = T\,(1 + 0.2 M^2)\). The skin only gets most of that rise, so engineers multiply the \(0.2 M^2\) by a factor a bit under 1. The widget uses \(T_{\text{skin}} = T(1 + 0.16 M^2)\), which also allows for the heat the black paint gives off.
- Black paint. A hot surface gives off heat at a rate proportional to \(\varepsilon\,T^4\), with \(T\) in kelvin. Black paint has an \(\varepsilon\) near 1 and bare metal a much smaller one, so the black skin shed heat faster and ran cooler.
- Thermal expansion. A length \(L\) heated by \(\Delta T\) grows by \(\Delta L = \alpha L \Delta T\). For titanium, \(\alpha \approx 9 \times 10^{-6}\) per °C:
\[ \Delta L \approx 9\times10^{-6} \times 32.7\ \text{m} \times 280\ ^\circ\text{C} \approx 0.08\ \text{m} \]Atoms are held by bonds that resist squeezing more than stretching. A hotter atom jiggles harder, and because the bond is easier to stretch, the atom spends more time farther from its neighbours.
- The inlet. The Blackbird's inlet slowed the air in steps. The slanted shock off the spike and its reflections inside the cowl slow the air while it is still faster than sound. The straight-across shock just behind the narrowest point, called the throat, makes the air slower than sound. Behind that shock, the widening duct slows the air further, and the pressure rises: at cruise the inlet squeezed the air about 40 times.
- Why the throat must shrink. Faster air needs a smaller throat to be slowed gently. If the throat is too wide, the last shock sits farther back, where the air is faster, and the shock wastes more energy. If the throat is too narrow, not all the captured air fits through, the pressure builds up, and the shock is pushed out the front: the unstart.
- Part jet, part ramjet. At high speed, much of the air went around the engine's core through ducts, straight into the afterburner. The engine kept running, but most of the push came from air squeezed by the inlet and burned in the afterburner. Engineers called the engine a turbo-ramjet.
The leak, explained
Now you can explain the puddles. At Mach 3, squeezed air heats the skin to around 300 °C, and the heating grows with the speed squared.
Hot titanium grows, so the panels were fitted loosely and the tanks leaked on the ground. Titanium stays strong when hot and weighs far less than steel. JP-7 fuel wouldn't catch fire beside the hot skin, and the fuel cooled the plane before burning. The early tanker meeting came from taking off light, not from leaks. And the spike you steered slowed the air until the inlet itself made most of the push.
Where it shows up
Anything long that heats and cools has the Blackbird's problem. Look at a big road bridge, and you may spot steel teeth across the road at each end:
An animation of a finger joint at the end of a bridge, seen from above. Two decks meet with interlocking steel teeth. Through the seasons the decks grow and shrink, and the teeth slide past each other. The animation plays by itself in a loop, from winter to summer and back. A bar at the top shows the temperature. The joint holds still for a moment in summer, when the teeth reach deepest.
Text version
Two bridge decks meet at a gap. Each deck end carries a row of steel teeth, and the teeth of one deck fit between the teeth of the other. In winter the decks shrink, the deck ends move apart, and the teeth overlap only a little. In summer the decks grow, the deck ends move toward each other, and the teeth slide deep between each other. The road surface stays continuous in every season, so cars roll across.
- Bridges: a steel bridge 100 m long grows about 6 cm between a cold winter night and a hot summer day, a swing of about 50 °C.
- Railway tracks: on very hot days, long welded rails can buckle sideways. Railways lay welded rail stretched, or at a chosen warm temperature, to keep the rail straight.
- Concorde: the passenger jet flew at Mach 2 with an aluminium skin and stretched by roughly 15 to 25 cm in flight, by most accounts.
- Spacecraft coming home: at about 25 times the speed of sound, the same squeezed-air heating reaches well over 1,000 °C, so capsules and the Space Shuttle used heat shields and tiles instead of bare metal.
Where to go next
One leaking plane opens a lot of doors. Here are the questions worth chasing next:
- Why does a spacecraft coming home get far hotter than the Blackbird, and why aren't heat shields made of metal?
- Can an engine with no spinning parts at all, called a scramjet, push a plane past Mach 5?
- Why exactly do atoms take up more room when they are hot?
- Why does an ordinary jet engine need the air slowed below the speed of sound?
- How do engineers pick a material that stays strong for hours at high temperature?
What to learn next: heat and thermal expansion first, then energy of motion and energy conservation; most high school physics courses cover all three. After those, look up "stagnation temperature" and "shock waves" for the flight side, "creep" for how hot metals slowly stretch, and "thermal protection system" for heat shields.
To see the Blackbird's engineering in moving pictures, watch Real Engineering's tour of the plane:
Ask Phy
- Why does squeezing air make the air hot? Explain with a bike pump and the Blackbird.
- How much does a 1 km steel bridge grow from winter to summer? Walk me through ΔL = αLΔT.
- What is a scramjet, and why is Mach 5 so much harder than Mach 3?
- Design and Development of the Blackbird: Challenges and Lessons Learned (P. W. Merlin, NASA, AIAA 2009-1522) — Skin temperatures, titanium share, JP-7, TEB, the inlet's share of the push, the drill bits.
- SR-71 Blackbird (NASA Dryden fact sheet) — Cruise speed, size, takeoff and fuel weight.
- Lockheed SR-71 Blackbird (Wikipedia) — Loose panels, the refuelling misconception, unstarts, the 1976 record.
- SR-71 Blackbird (Lockheed Martin history) — Kelly Johnson's quote, cadmium tools.