A little-known fact about orbital rocket engines is the size of their second or upper-stage nozzles, which are much larger than those used by sea-level engines. There is a good reason for this substantial size difference.

A vacuum-optimized rocket engine nozzle is bigger than a sea-level nozzle as it needs to match the significantly lower air density in the upper atmosphere and the vacuum of space. The hot exhaust gases exiting a rocket’s nozzle need to equal the external air pressure to maximize engine efficiency.

The rocket engine nozzles visible below any launch vehicle during liftoff, whether one or multiple nozzles are all part of the first-stage section of a rocket. These engine nozzles are all optimized to operate low in the atmosphere at high ambient pressures.

Hidden higher up below the surface structure of a rocket sits the second-stage rocket engine, which is connected to a much larger nozzle. This nozzle is optimized to operate higher up in the atmosphere as well as the vacuum of space.

(It has to be noted, though, that the nozzles of a rocket form only part of a much larger & complex launch vehicle. Learn more about what exactly an orbital rocket is and how it functions in this article.)

The following section describes in more detail why the upper-stage nozzle of a rocket engine is that much bigger than its sea-level counterpart and the importance of this size difference.

Why Vacuum Rocket Engine Nozzles Are Bigger Than Sea Level Engine Nozzles

Vacuum Optimized Vs Sea Level Optimized Nozzle
A sea-level optimized Raptor nozzle (on the left) stands next to a vacuum-optimized Raptor nozzle (on the right) at the SpaceX development facility in McGregor, Texas. – Image Credit: SpaceX (via Twitter)

For a rocket engine to operate at its most efficient level (in other words, produce the maximum amount of thrust), it is crucial for the hot gases exiting the engine nozzle to match the external air (or ambient) pressure.

Complicating matters for engineers striving to achieve nozzle exit pressures consistently equal to the ambient pressure is that a launch vehicle has to travel through the Earth’s atmosphere, where the air pressure decreases dramatically from sea level to space.

At sea level, the air pressure is around 1 000 millibars. It quickly decreases with altitude to 100 millibars at 12 km and only 1 millibar at 50 km. This makes it impossible for one single nozzle design to maintain maximum efficiency throughout a launch vehicle’s ascent.

Fortunately, the principles of fluid dynamics dictate that the pressure of rocket exhaust gases decreases as the surface area of a nozzle increases without a loss in velocity. This means that the bigger (or more expanded) a rocket nozzle is, the lower the gas pressure.

As a result, the first-stage engine nozzles of a rocket (visible underneath a rocket during launch) are smaller than upper-stage nozzles, which are significantly bigger to allow the pressure of the gases exiting the nozzles to decrease enough to match ambient pressures.

This configuration allows the smaller first-stage nozzles to operate at maximum efficiency in the dense atmospheric air close to the surface, while the larger second-stage nozzles are deployed in the upper atmosphere, where the thinner air allows optimal operation.

(Second-stage rocket booster typically deploys at a height of 50 – 80 kilometers or 31 – 50 miles above the Earth’s surface. At this altitude, the air pressure is 0.1% or less than the air pressure at sea level.)

It’s important to note, though, that the majority of rocket engine nozzles are a compromise, as, at some point, they travel through parts of the atmosphere where the pressure of the gases exiting the rocket’s nozzle will not exactly match external air pressures.

For example, the Space Shuttle’s three main engines and the Delta IV rocket engine used nozzles that were overexpanded during launch (resulting in a pattern of recompressing & decompressing shock waves), which pressures equalized as the rockets gain altitude.

In contrast, all engine nozzles, including vacuum-optimized nozzles, are under-expanded in the vacuum of space. In order to match the non-existent air pressure, a rocket’s nozzle technically needs to expand infinitely to “match” external pressures.

Delta IV Heavy Nozzles During Liftoff
The overexpanded nozzles of a Delta IV Heavy rocket firing liftoff, displaying the familiar recompressing & decompressing shock waves in its exhaust plumes.

Clearly, this is not possible, and as a result, it is normal to see a rocket engine nozzle’s exhaust plume expand far beyond the width of the nozzle in the upper atmosphere and space, resulting in a decrease in engine efficiency.

Much research and development time is spent on designing & modifying engine nozzles to ensure the pressure of hot gases exiting a nozzle matches the ambient pressure. And there is a good reason for this, as the next section will explain in more detail.

Why Rocket Exhaust Plume Pressure Needs to Be Equal To External Air Pressures

Under Expanded Ambient Overexpanded Nozzle
Diagram showing the different effects an under-expanded, ambient, and overexpanded nozzle has on the way a rocket engine’s exhaust plumes interact with the external air pressure.

Successfully placing a rocket into orbit is all about getting a launch vehicle off the launchpad and into space as quickly and efficiently as possible. This means creating the maximum amount of thrust while using the least amount of fuel in the process.

Obtaining maximum efficiency is also the primary reason why engine nozzles are designed in such a way that the pressure of the hot gases exiting the nozzle matches the external air pressure at any given altitude.

When the exhaust gas pressure of an engine nozzle matches the ambient pressure, maximum thrust and energy efficiency are achieved.

More simply put, if the exhaust plumes from a nozzle push out in a straight line without expanding beyond the edge of the nozzle or being compressed by the external air pressure, the rocket engine is functioning at its optimal level.

As the diagram above illustrates, a nozzle can be in one of three states, depending on nozzle size and the external air pressure at a given altitude:

  1. Under-Expanded Nozzle
  2. Ambient Nozzle
  3. Overexpanded Nozzle

An Under-Expanded Nozzle produces exhaust gases with a higher pressure than the ambient air, resulting in the exhaust plumes extending beyond the edge of the nozzle, which decreases efficiency. Vacuum-optimized nozzles typically display this characteristic.

(As a significant portion of the gases traveling at supersonic speeds flows more towards the side than through the back of a nozzle, it leads to some loss in thrust. As a result, the engine has to work harder and burn more fuel to compensate for the lost energy.)

Saturn V Rocket
A Saturn V rocket’s nozzles became under-expanded at high altitudes.

An Ambient Nozzle produces exhaust gases with a pressure equal to the ambient air, resulting in the exhaust plumes extending in a relatively uniform fashion, which allows the engine to operate at maximum efficiency.

An Overexpanded Nozzle produces exhaust gases with a lower pressure than the ambient air, resulting in the exhaust plumes being compressed by the external air pressure, which decreases efficiency. Many sea-level optimized nozzles display this characteristic.

(Since the pressure of an overexpanded nozzle’s exhaust plumes is less than the atmospheric pressure, some air is allowed to enter through the side of a nozzle, which disrupts the gas flow, a process known as flow separation.

Not only does this disruption result in a loss of efficiency, but the instability in the gas flow and resulting lateral forces can also damage the nozzle itself.)

Although it is practically impossible for an engine nozzle to match the external air pressure throughout its ascent, it is clear that keeping the exhaust gas pressure as close as possible to ambient pressure results in the most efficient engine operation producing the most thrust.

Conclusion

As a rocket travels through the atmosphere, where the air pressure changes dramatically with altitude, using different-sized nozzles for different heights doesn’t just make sense, it’s necessary for maximum efficiency.

As this article illustrated, having a much larger vacuum-optimized engine nozzle allows a rocket’s second stage to function optimally in the upper atmosphere and space, while the smaller first-stage nozzles operate more efficiently at sea level.

This article was originally published on headedforspace.com. If it is now published on any other site, it was done without permission from the copyright owner.

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