# Are rockets faster than airplanes?

Rockets are fast. Faster than anything else somebody could fly with - at least intuitively to me.

But - airplanes are fast too.

A rocket typically flies vertically, an airplane mostly horizontally.

And going up is much harder than just going forward. A rocket is certainly faster than other ways going up - that does not mean it is fast when compared to something different, a plane in horizontal flight.

Of course, a rocket can end up faster than a jet outside the atmosphere.

But when I think of a rocket that is still in the atmosphere, or one I can still see from the ground: Is that really "faster than an airplane"?

• Think about military anti aircraft rockets, both air-air and ground-air. They would be useless if they were slower than airplanes. Within the atmosphere and horizontally. – Uwe Jul 23 at 13:33
• The SR-71 could fly higher than the anti aircraft missiles of that time. But it would been possible to build a rocket flying fast and high enough. The first stage of the Saturn V reached a hight of 65 km and a speed of 2390 m/s, that is Mach 7.24. All in only 2.5 minutes. – Uwe Jul 23 at 13:58
• The SR-71 success was mostly a factor or interception time: by the time the radar had a firing solution, the missile would run out of fuel before it could make the intercept. – Hobbes Jul 23 at 14:46
• We've produced rockets that can go from zero to Mach 8 in about 1 second to intercept incoming ballistic missile warheads in the final stage of flight. I am not aware of any plane with comparable performance. – TemporalWolf Jul 23 at 20:23
• Also, just to dispel one particular misunderstanding, rockets fly horizontally as well. The knack to getting to space is to go sideways really fast, not to go up really far. – Williham Totland Jul 23 at 20:29

Rockets are much faster than airplanes for most of their flight.

Here's a graph of a Space Shuttle launch:

The red line is speed. It's in ft/s, 1000 ft/s is 1097 km/h. So At about 45 seconds, the Shuttle flies 1000 km/h which is faster than an airliner.

At about 1:40 it crosses 3000 ft/s which is about Mach 3 (the speed of the fastest aircraft). Altitude is then 140 kft or ~ 30 km, higher than an aircraft can fly.

The final speed needed to get into orbit is about 8 km/s or Mach 25.

It doesn't look fast because at the same time, it quickly gains altitude. This makes its speed difficult to judge from the ground.

• The speed of the fastest aircraft is Mach 3.32 - that does not change anything, of course. The SR-71 Blackbird has a cruise speed of Mach 3.2, an official max speed of 3.32 (and can probably fly somewhat faster, but that's classified (Important during the cold war). 4000 km/h - mind bending. – Volker Siegel Jul 23 at 7:59
• The X-15 is faster than the SR-71.If you need an air-breathing engine and a lower maximal altitude, the X-43 is faster than the SR-71 (yet, the space shuttle than can also be considered as an aircraft for some of its flight is still faster) – Manu H Jul 23 at 12:46
• Feet per second? Seriously, after losing their \$125 million Mars orbiter to metric/imperial unit conversion error, I would expect NASA to have learned their lesson. – Tomáš Zato Jul 23 at 14:48
• @TomášZato this chart was not made by NASA – Tim Jul 23 at 14:59
• @VolkerSiegel that graph only shows the first part of the ascent while the SRBs are burning. The shuttle ultimately accelerates to about 27,000 km/hr to achieve orbit. – alex.forencich Jul 23 at 22:29

A rocket isn't automatically fast - a small firework rocket may be no faster than a car. The important point is that rockets carry their own oxidiser and aren't limited by the need to interact with the air.

Most aircraft engines need to develop lots of thrust at low speed for take off, and they have propellers or large fans that cause drag at high speeds, limiting them to sub-sonic speeds. Even a pure turbo jet engines has a compressor to suck in air at low speed, which causes drag that limits them to about Mach 2 or 3.

A ram jet doesn't have these limits, how ever it has to slow down air as it enters the engine to give it time to mix with the fuel and burn. This limits them to about Mach 7. (There is research into super-sonic-combustion-ramjets (SCRAM jets) that could theoretically go faster but so far only a handful of development flights.)

A rocket doesn't have that limit, it will keep accelerating until it runs out of fuel (which typically doesn't take long, as they're really inefficient compared to air-breathing engines).

• Jaxa has flown an air-breathing rocket... – JCRM Jul 23 at 17:52
• @JCRM - How do you define an "air breathing rocket"? I've always known the definition of rocket engine/motor to be carrying all of its propellant (oxidizer and fuel, or just fuel, if monoprop). – Carlos N Jul 23 at 21:05
• @CarlosN An Air-augmented rocket? Or, technically, a water rocket... – Chronocidal Jul 24 at 10:07
• @CarlosN Good question, and one that deserves more than a comment. Go ahead and ask this as a new question. – Hobbes Jul 25 at 6:38

Rockets don't actually mostly go up, they try quite hard to go up as little as possible.

While flying, gravity is always accelerating you downwards at 9.8 m/s^2. This means that any fuel spent accelerating upwards is wasted, as gravity will pull you back to earth eternally, no matter how much fuel you burn (unless you reach escape velocity, but it will still slow you down substantially by the time you've escaped). This is not the case with horizontal velocity, which is completely unimpeded in a vacuum, since the only force acting on your vessel is a central force towards the center of the earth, perpendicular to the tangential direction.

An orbital launch vehicle's primary goal is to reach orbit, which requires a horizontal velocity high enough that the earth's curvature falls away from you at the same rate you're falling towards the earth. This velocity is around 7.5 km/s in low earth orbit, many times faster than even the fastest aircraft ever built.

Unfortunately the atmosphere gets in the way of maintaining such velocities close to the ground, so rockets do have to waste a bit of fuel in order to climb above it, but the vast majority of their fuel is spent accelerating sideways. You'll notice that upon launch, rockets almost immediately tip over slightly, and slowly turn towards the horizon as they loft their trajectory above the atmosphere and no longer require as much thrust to prevent gravity from halting their upwards velocity and pulling them back downwards.

• There is no escape from gravity by accelerating horizontaly. Before reaching an orbit a decreasing part of the thrust must be used to keep the height already reached. Going hypersonic within the upper atmosphere would require a heavy heatshield for the rocket. – Uwe Jul 25 at 7:48
• @Uwe That would seem to depend on your definition of horizontally. Let's say (numbers out of thin air here, and simplifying massively to make this fit within 600 characters) that a rocket climbs strictly vertically to 10 km, then starts its gravity turn, which results in a flight path at 90° to the initial vertical ascent when at an altitude of 20 km above a hypersimplified spherical Earth, then continues to fly at the tangental angle thus obtained. Such a rocket could be said to move strictly horizontally, but it will also be gaining altitude as the ground under it falls away. – a CVn Jul 25 at 11:46
• "Rockets don't actually mostly go up, they try quite hard to go up as little as possible." - #NotAllRockets - Javelin anti-tank missile goes up & down. – Cees Timmerman Jul 25 at 13:52
• gravity is always accelerating you downwards at 9.8 m/s^2 is not entirely true, that is the acceleration rate at the surface. At 30k ft, it about 0.02 lower, at 1000km its only 7.3 m/s^2 – rtaft Jul 25 at 17:29

That depends entirely on what rocket and airplane you are comparing, of course.

However, with regard specifically to the large rockets used for spaceflight against commercial aviation, yes. Orbital speed is approximately 8 km/s for Earth at a low orbit. A typical commercial jetliner flies at speeds of around 0.25 km/s. That's all it takes to know which is "faster".

How fast things "appear" to be moving, however, is a rather different matter, and a huge function of observer perspective. "Apparent" motion is really the crossing of your visual field at a given rate, and this can be seen by noting that it is not measured in units of physical speed (m/s, km/s, km/h, MPH, etc.) but in units of angle per time, e.g. rad/s, mrad/s, deg/s. This depends on all of:

• the actual speed of the object,
• the distance to the object from your observing point, and
• the angle its trajectory makes with the line from your eyes to it.

. Note that as the distance is changing, so too will the apparent speed through the course of the flight: think about a car going by you - its apparent speed is fastest at closest approach when it passes your perpendicular to the roadway, and then slows as it recedes.

The relevant expression can be derived from trigonometry: it is

$$\mbox{Visual speed} = \frac{\mbox{Actual speed}}{\mbox{Observer distance}} \cdot \sin(\theta)$$

where $$\theta$$ is the angle in the third bulletpoint. Note that the visual speed is, as just mentioned, maximized when moving perpendicular to your line of sight, i.e. $$\theta = 90^{\circ}$$ or $$\frac{\tau}{4}\ \mathrm{rad}$$.

So an airplane at a distance of 10 km above your head, looking straight up and traveling at 0.25 km/s horizontally, has an angular speed of 0.025 rad/s or 25 mrad/s. A rocket which is maybe about 50 km up and going 2 km/s, say, would have an angular speed of 40 mrad/s if it were traveling similarly transversally, but if the angle to your vision is, say, 250 mrad (approx. $$14^{\circ}$$) as may be expected from an upward trajectory, then it will only have an apparent speed of 10 mrad/s, less than half as much. This is why a rocket appears slower, as you observe, during the launch phase.