We all love to watch a rocket launch into space. But, the rocket structure analysis that makes a successful launch possible goes unnoticed.
I’m going to go over the more interesting aspects of rocket structure analysis. This way we better appreciate how we fire large metal cylinders into Earth’s orbit. A distance of 100 plus miles above the ground in only 8.5 minutes.
These are rockets weighing 6 million-plus pounds and traveling 17,600 miles per hour.
It’s incredible how we get so much mass moving this fast in so little time.
#1 Component and system analysis
You never want to leave anything up to chance in rocket design. The margin for error is incredibly small.
This is why every component and system of a rocket is heavily analyzed.
When I first set eyes on the rigid design requirements in the analysis I became overwhelmed. But, it made sense. We’re shooting a huge metal canister into space.
Some of the analysis types include:
- Fatigue and fracture
- Shock and vibration
These tests all vary too depending on the material, placement, and component shapes. For example, rocket engines have their own design criteria compared to rocket frames.
Important note: the analysis changes if a rocket needs to carry humans. Humans add an entirely new variable to rocket design.
Failure Mode, Effect, and Criticality Analysis (FMECA)
Let’s dive deeper to better understand how the analysis works.
For starters, all companies use some version of FMECA. In rocket structure analysis, FMECA is the foundation of good design.
It’s a reliability procedure to identify possible failure points. Every component and system of a rocket goes under the microscope. No stone goes unturned.
The goal is to calculate the fault tolerance of all components and systems.
Fault tolerance: think of it as a function of three main parts. For a rocket we have:
- Vehicle integrity
- Mission success
- Crew safety.
Thus, if a component fails, how likely is it the mission will still succeed? On the flip side, if a component fails and the vehicle goes unharmed, will the crew remain safe?
This then ties into the probability of failure. A component with a high chance for failure becomes a big cause for concern.
To illustrate this, imagine a component inside of a rocket engine. If this component fails, the rocket would turn into a ball of flames.
Without question, this component receives the highest level of criticality.
Important note: Critical Items List (CIL) goes in hand with FMECA. Items on this list go through the following checks:
- Rigorous analysis
- Quality control
- Manufacturing improvement processing
- Constant maintenance servicing
#2 Factor of Safety (FoS) margins
What is FoS? it’s the safety factor used in structural analysis. The FoS tells you how much stronger a structure is than required for a given load.
You can find FoS values in various codes and standards for different structures. While keeping in mind, the calculation for the FoS isn’t an exact science. Especially for large and complex projects.
But, engineers always do their best to calculate the FoS to a reasonable accuracy. Plus, they consider past failures and use their years of experience.
I find the FoS is proportional to your uncertainty. What I mean is, the better you can predict your load and materials, the need to use an FoS decreases.
So, loads are arbitrarily increased when an engineer is unsure of the max load. In return, the FoS increases.
With rockets though, it’s always preferred to use a low FoS when possible. A low FOS requires thorough structural analysis with rigorous testing.
This may sound counter-intuitive given the stress placed on a rocket in a launch. But, there’s a method to this madness.
FoS with rocket structure analysis
Yes, it’s preferred to use a low FoS with rockets. Thus, rocket components ride a fine line between working and failing.
The driving reason comes from a rocket’s weight. The lighter, the better. But why?
In 2008, NASA said it costs $10,000 to put 1-pound of payload in Earth’s orbit. So clearly, it’s in everyone’s financial interest to keep a rocket’s weight down.
For this reason, NASA typically uses a 1.25 FoS for expendable launch vehicles. Thus, these NASA rockets will fail at 1.25 times the design load.
Of course, if humans are on board, the FoS would increase.
All this is significant when you consider going from an FoS of 2 to 1.5 cuts back on around 1,000 pounds of weight.
Important note: even SpaceX’s reusable rockets are not completely reusable. Certain components need replacement around 10 or so flights.
Then, other components need weeks of service. Without this touch-up work, the designed FoS would dip a lot. Not what we want.
All that said, Space X’s Falcon Heavy advertises $3,100 per pound to orbit. As technology further advances, this cost will continue to drop.
#3 Rocket load analysis
Let’s go over some of the load testing done with rockets. This way we can better appreciate the work required to send a rocket into space.
1) Thermal gradient testing: testing the internal and external skin of a rocket. This checks the effects of thermal gradients.
In other words, testing the extreme temperatures a rocket will experience in flight. The hottest and coldest temperatures.
2) Pressure testing: checking for strains on a rocket’s frame due to pressure. Engineers do this test by creating internal and external pressure variances.
This involves repeated depressurizations and repressurizations to simulate a liftoff. Also, to simulate the entry into space and back into Earth’s denser atmosphere.
This test also captures the max pressure a rocket will experience.
3) Load testing: testing at the designed load. Then, testing to the max expected load.
Rocket load sources include:
- Aerodynamic drag loads.
- Ambient temperature.
- Engine vibrations.
- Gimbaled thrust. Where the exhaust nozzle of a rocket swivels from side to side relative to the rocket’s center of gravity. This creates a nonuniform thrust.
- Rocket acceleration
- Thermal expansion. Both transient and steady-state.
- Transient dynamic loads. For example, thrust asymmetric flow. The many engines of a rocket will not always be firing uniformly.
Also, engineers run extra tests when a component meets any one of the following criteria:
- A component has a high criticality of failure.
- The analysis leads to uncertainty. This typically happens when there’s a high number of variables involved.
- The minimum set fatigue margin is not met. We’re looking for how long a component will last after repeated use before issues come up.
In short, engineers need to run tests with all these variables considered. Then with each test, load levels are incrementally increased. They’re increased until a component fails.
Each incremental step measures strain limits on individual rocket parts. This helps to determine critical items in a rocket’s design.
#4 Rocket material selection
Let’s now jump into the meat of rocket structure analysis.
The structure of a rocket is to create a load-bearing frame. Think of an airplane’s fuselage as a good comparison.
So, a rocket’s frame holds the rocket together against all loads and stresses. All the while safely carrying:
As you could imagine, selecting the right material is a tall order. Just look at this heavy list of requirements:
- Sustain high forces during max aerodynamic pressure in launch and ascent.
- Withstand very low temperatures in a rocket’s liquid fuel systems. Cryogenic propellants like liquid hydrogen are often used. Temperatures here reduce down to -253°C or -423°F.
- Withstand extreme high temperatures in a rocket’s combustion chamber and exhaust area. Temperatures reach as high as 2,760°C or 5,000°F. Even more, methane engines can reach temperatures near 6,000°F. As a comparison, the temperature of the surface of the sun is 10,000°F.
- Tolerate hydrogen embrittlement with the usage of hydrogen propellant.
- Remain lightweight to limit propellant.
- Strong enough to carry max load, while not buckling from launch and ascent stress.
What’s more? An engineer needs to consider all these variables together.
For example, a frame must sustain pressures at cryogenic temperatures inside propellent chambers. At the same time, endure scorching temperatures inside combustion chambers.
While also withstanding varying mechanical loads. All this and much more happens in a launch.
If that wasn’t enough, a rocket needs to have an aerodynamic shape.
Let’s go over what’s involved to achieve this near-impossible feat.
Material selection goals for rockets
The goal is to select a material with the following properties:
- Certain stiffness
- High strength
- Resilient to extreme temperatures
To pull this off, the materials of choice for rocket frames are:
- Aerospace-grade aluminum
- Aerospace-grade titanium
- Stainless steel 301 (Elon Musk’s material of choice for Space X’s Starship rocket)
These are all high-density metals. You can make them very thin while maintaining their strength. This is key!
I’ll summarize other key advantages of high-density metals by looking at other materials:
- Low-density metals compared to high-density metals have a lower melting point.
- Low-density metals have a high chemical reactivity. This makes them not suitable for all phases of propellant usage. Thus, their inability to tolerate contact with cryogenic fuels and hot exhaust gases.
- Composites and ceramics are high strength and chemically stable materials. But, they can’t handle extreme temperatures. Also, they’re often too frail to handle the mechanical loads of a launch. Think of the compression, tension, and bending that comes with a launch.
#5 Rocket mass ratio
A critical rocket design element is the mass ratio. The ratio of fuel carried by a rocket to the mass of the rocket itself.
To better understand the mass ratio, we need to look at a rocket’s velocity. With a greater mass ratio, a rocket will achieve a greater change in velocity (delta-v).
To that end, to reach low Earth orbit, a rocket needs to travel 7.8 km/sec.
Thus, from standstill on a launchpad, a rocket needs a delta-v of roughly 10 km/sec. This delta-v value considers the force of drag and gravity on a rocket. That’s why we used 10 km/sec versus 7.8 km/sec.
Now, using Tsiolovsky’s rocket equation, we’ll do a mass ratio calculation. This will further highlight the engineering challenges of rocket design too.
Tsiolkovsky rocket equation
This equation relates the max change of a rocket’s speed with no external forces applied. That said, the equation considers two critical variables:
- Exhaust velocity from a rocket’s nozzle. A rocket expels a certain amount of gas at a certain rate. This is the energy that propels a rocket upwards.
- The initial and final mass of a rocket.
= initial total mass of a rocket (includes rocket propellant)
= final total mass of a rocket (without rocket propellant)
= ejection speed of exhaust gases out of a rocket’s nozzle
Let’s discuss our inputs:
- To reach Earth’s low orbit, an object needs to travel to an altitude of 200 km while traveling 7.8 km/sec.
- Delta-v will be between 9 to 10 km/sec. As I mentioned, we increase the 7.8 km/sec to account for gravity and air resistance in a rocket’s ascent. We’ll use 9.9 km/sec.
- Exhaust velocity depends on the chemical propulsion system selected. For example, a kerosene-oxygen mix produces an exhaust velocity of 3.1 km/sec. Where a hydrogen-oxygen mix produces an exhaust velocity of 3.4 km/sec. We’ll use the 3.4 km/sec.
Now, we calculate the percentage of rocket mass that’ll be fuel:
This result means 94.55% of this rocket is fuel. So astronauts that board a rocket are sitting on top of a missile. Scary yet amazing!
Fuel weight of NASA’s Saturn V Rocket
To put things into perspective, let’s look at NASA’s famous Saturn V rocket. From 1967 to 1973 the Saturn V supported the Apollo missions for moon exploration.
The first stage of this rocket carried 203,400 gallons of kerosene fuel. Also, 318,000 gallons of liquid oxygen for the combustion.
All in all, the Saturn V rocket was 85% fuel.
To further drive the point home of this huge mass ratio discrepancy, let’s look at a real-world example.
- A regular 12 oz soda can is 94% soda
- A NASA shuttle external tank is 96% fuel
Pretty amazing, given you hold and drink from one can. While the other we launch into space.
Rocket speed with rocket mass considered
To analyze a rocket’s mass from a different perspective, let’s focus on . To escape Earth’s gravity, a rocket needs to travel 10 km/sec as we learned.
We’ll again use the same equation as we did above. So with a rocket at rest, the change in velocity, delta-v, becomes the final velocity.
Important Note: this equation as setup doesn’t consider air resistance and gravity in a rocket’s launch and ascent.
Our focus is on , the mass of a rocket without propellant. As the value increases, the natural log ratio of and decreases. In return, our final velocity, , decreases.
All things considered, in increasing , the stored fuel, , would need to increase. So, the cost of a launch increases substantially.
This is why engineers want to keep the weight of a rocket weight low.
At the end of the day, if the dollars and cents don’t agree, nothing will get done.
#6 Rocket geometry
The structure of every rocket you see is long, thin, and tube-shaped. What’s amazing is, part of this design is nature-inspired.
I’m talking about a rocket’s nose cone. It’s one of the strongest architectural shapes you can find in nature.
A rocket’s nose cone and the unbreakable egg
Think of what you eat for breakfast. Eggs!
Try squeezing an egg between two of your hands. Press along the egg’s long axis.
It’s near impossible to break the egg. Yes, it’s hard to imagine given how easily we crack several eggs when we’re hungry.
So, what’s the secret behind eggs? Eggs have a certain curvature without angles.
Thus, when you place an even force on an egg’s domes, the force spreads out. The force then goes down the sides of the domes distributing evenly.
As a result, an egg experiences less stress and strain. This is why we love the shape of eggs.
Now taking a page from nature, we’ve shaped the dome of rockets like eggs. This helps rockets pierce our atmosphere at supersonic speeds without cracking.
Rocket’s small diameter frame
A small diameter frame helps a rocket reach supersonic speeds. The logic behind this design is pretty straightforward.
Just think of an arrow that cuts through high winds with ease.
What I’m getting at is, the larger the frame diameter the greater the drag. This is because a rocket will need to push more air out of the way to climb higher.
Now, drag relates to the cross-sectional area of an object that pushes through the air. So, the more narrow a rocket is, the less drag it’ll experience.
Try adding an umbrella to the end of an arrow and then shoot it. I’m sure you can guess the outcome.
Rocket equation for drag
Let’s look at the math now:
= drag force
= drag coefficient
= cross-sectional area. In our case, a rocket’s front nose cone’s surface area.
= density of fluid. In our case, air.
= speed of a rocket relative to air.
As a reference, a flat plate object will have a of 1.28. Where a nose cone object will have a of 0.295. Of course, assuming both objects have the same frontal area.
Knowing this, we see as increases, increases too. Thus, to keep reduced we need to keep to a minimum.
Important note: the drag coefficient is commonly calculated experimentally. This experiment happens inside a wind tunnel supported with computational fluid dynamics analysis.
So, is a complex value with many variables in its function.
That said, models how an object’s shape and airflow conditions affect drag. This model considers the effects of air viscosity and compressibility too.
Also, different shapes have different drag coefficients. The shapes in our case are in reference to the egg-shaped frontal area of a rocket.
Let’s go one step further and look at the variable in our above equation.
You can see air drag increases with the square of your speed. Now, here’s the very cool part.
If you accelerate too quickly, you’ll burn too much fuel just to maintain a constant speed.
The trick is to accelerate slowly after launch. Then, as the air gets thinner the higher you go, to ramp up your speed. This will save you a lot of fuel.
#7 Rocket thrust
We can now better understand a rocket’s thrust with everything we learned so far.
Keep in mind, thrust is the force that moves a rocket through air and space.
With that out of the way, we know a rocket needs to travel very fast to reach orbital velocity.
To enter orbit around Earth, you need to reach a speed of around 17,600 miles per hour. This requires a lot of thrust.
Now, thrust depends on two variables:
- The amount and speed of gas a rocket fires out from its exhaust nozzle.
- The shape of a rocket’s exhaust nozzle, where the gas fires out from.
Also, the thrust force needs to be greater than a rocket’s weight. Another way to put it, the thrust force must overcome the force of gravity that pulls a rocket down.
Finally, the thrust force must overcome air resistance too. So, the less a rocket disturbs the air, the less drag it’ll create. In return, the less energy a rocket will lose to overcome drag.
This is why a rocket’s geometry is critical as we discussed in the previous section.
Let’s look over some equations again to better understand what’s going on.
Rocket equation for thrust
First, we’ll rearrange an equation we already used. We’ll solve for .
As increases, decreases given all other variables remain constant. This tells us heavier rockets require greater exhaust velocity.
Now, let’s look at how to calculate rocket thrust:
F = amount of thrust produced by a rocket.
= the rate of ejected mass flow. So, the amount of gas that passes through a rocket’s nozzle per unit of time.
= ejection speed of exhaust gases out of a rocket’s nozzle.
= pressure of exhaust gases.
= pressure of ambient atmosphere.
= the area ratio of a rocket’s nozzle’s throat to exit. Where a rocket’s throat is the smallest cross-sectional area of the nozzle.
Looking at both equations together now, and decrease with a heavier rocket frame.
What does this tell us? A rocket with these specs won’t be able to enter orbit.
How to increase thrust with heavier rockets?
Looking at the last equation, you can probably think of two quick solutions on how to get the rocket into orbit.
The first solution of increasing : you can’t infinitely make the nozzle exit larger. It’ll only add weight to the rocket.
Also, the area ratio between the nozzle’s throat to exist has already been finely designed.
A fine balance exists between and the amount of fuel carried. What I mean is, for a given rocket to get into orbit, engineers have already considered almost all designs.
Engineers have near perfected the design of against the max rocket weight. So you can’t double the max payload and think adjusting alone will get you into orbit.
The second solution of increasing : is a function of the engine and chemicals used. Assuming the nozzle size remains constant.
That said, we’ve already investigated near all chemical propulsion systems. Thus, more than likely we can’t increase with the chemicals used today. Rocket engine tech will improve overtime though. Nothing world-changing.
So, what’s left? How else can we create more thrust to get a heavier rocket into space?
Either nuclear propulsion becomes a viable tech, or we increase the propellant. In the end, it seems the answer always defaults to more propellant.
To summarize, a heavier rocket today needs the following:
- More propellant
- The propellant exits faster from a rocket’s nozzle
- A combination of more propellant that also exists faster from a rocket’s nozzle
Important Note: different fuels generate differing amounts of energy and at varying rates. This all requires consideration when choosing the fuel type to use for a given rocket.
#8 Important rocket design considerations
I’m going to go deeper into some more interesting rocket design considerations. These elements will further show the complexity of designing a rocket. Not that you need any more convincing.
Axial force and bending moment
When you apply an external force or moment to a solid structure, it’ll bend. So, think of the bending moment as the reaction induced in the structure.
As an extreme example, imagine a palm tree when a hurricane hits. The solid tree trunk will completely bend from the force of the wind.
Going back to rockets now. When a rocket ascends it doesn’t shoot straight up.
Rather, it has a tilt as it ascends. This steering technique allows a rocket to preserve fuel. Also, to reduce stress and strain on the frame.
As with anything though, this tilt brings new problems. The tilt causes an axial force and bending moment.
A rocket’s thrust, drag, and weight generate the axial force. While the rocket moving at an angle in the air creates the bending moment.
Important Note: the bending moment force compresses one side of the rocket. But also, causes tension on the opposing side. Imagine what happens when you bend a drinking straw.
This further adds to the complexity of rocket structure analysis. Just another one of many variables thrown into the bag for an engineer to piece together.
To better understand, let’s view the complete line load equation for a rocket. It’s a simplistic way of analyzing the acting forces.
Complete line load equation
= ultimate tensile line load
= axial force
= shear force
M = moment
R = rocket radius
Looking at the equation, as and increase, increases. Thus, the following rocket design elements need to consider these forces:
- Selected material
- Rocket wall thickness
- Rocket shape
Without proper engineering, a rocket will buckle from the stress. Then blow up given the amount of fuel a rocket holds.
You know, how a muscle car vibrates as you rev up the engine? Something similar goes on with a rocket.
Rockets powered by liquid fuel pump-fed rocket engines experience vibrations. You’ll find these vibrations on the vertical axis of rockets.
The vibration comes from the instability in the structure and propulsion system. The flow of propellant that feeds the engines causes what’s called thrust oscillation.
To tackle this problem, NASA now uses accumulators with their engines. This helps to suppress the vibrations.
But, vibrations also come in the liftoff stage from rocket engine noises. The emission of hot gases breaks the sound barrier causing shockwaves.
Keep in mind, a rocket produces a thrust of 7.5 million-plus pounds to shoot upwards into space.
In structural engineering, all components have flaws during manufacturing and service. In other words, all components will have some level of crack-like defects.
As you’d guess, the growth of cracks will reduce the life of any structure.
Think of an old building in your city that’s on its last leg. The foundation and structure have eroded. It’s a building you don’t want to call home.
In rocket structure analysis, it’s no different. In fact, structural integrity becomes an even greater concern as you’d guess.
This makes fracture control critical in controlling the effects of structural flaws. It’s a science and art.
So, space programs do tests in different extreme environments. These tests find weaknesses in components. For example, if a propagated crack could lead to mission failure or loss of life.
Rocket structure analysis wrap up
A rocket looks like a simple metallic tube that breathes out fire to fly into space. But, rockets are some of the most complex man-made machines.
It’s an understatement to say a lot goes into rocket structure analysis. Rocket design uses almost every type of engineering.
The amount of thought and effort to make a launch possible is mind-blowing. And I only scraped the surface.
For me, this makes every launch even more spectacular.
What’s more, with every launch we gather more data. Data on pressures, strains, stresses, temperatures, and vibrations on a rocket.
This data will only further improve rocket design.
I then hope one day we can reduce the price of a launch to fractions of what they are today. This will take us to a new age in space exploration.
What do you find most spectacular about rocket structure analysis? Where do you see rocket technology a decade or even a century from now?
Featured Image Photo Credit: NASA (image cropped)
SUBSCRIBE TO ENGINEER CALCS NEWSLETTER
Koosha started Engineer Calcs in 2019 to help people better understand the engineering and construction industry, and to discuss various science and engineering-related topics to make people think. He has been working in the engineering and tech industry in California for over 15 years now and is a licensed professional electrical engineer, and also has various entrepreneurial pursuits.
Koosha has an extensive background in the design and specification of electrical systems with areas of expertise including power generation, transmission, distribution, instrumentation and controls, and water distribution and pumping as well as alternative energy (wind, solar, geothermal, and storage).
Koosha is most interested in engineering innovations, the cosmos, our history and future, sports, and fitness.