8 Fascinating Things About Rocket Structure Analysis

Watching a rocket launch into space is amazing. But more amazing is the rocket structure analysis allowing for successful launches.

I’m going to go over the 8 most interesting parts of rocket structure analysis. You can then better appreciate how we fire large metal cylinders into Earth’s orbit. This is a distance of 100 plus miles in a trip taking only 8.5 minutes. If this wasn’t enough, these rockets weigh 6 million-plus pounds and travel 17,600 miles per hour.

#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 analyses I became overwhelmed. But, it all made sense. We’re shooting a huge metal canister into space. So it’s no surprise engineers do all the following types of analysis:

  • Stress
  • Fatigue and fracture
  • Thermal
  • Acoustic
  • Shock and vibration
  • Corrosion
  • Reliability

Important note: the analyses changes if a rocket needs to carry humans. The changes are to account for human safety by making the rocket more structurally sound.  

Failure Mode, Effect, and Criticality Analysis (FMECA)

spacex rocket at cape canaveral air force station
SpaceX rocket at Cape Canaveral Air Force Station (Photo Credit: SpaceX)

To expound on the analyses, let’s discuss FMECA. For starters, all aerospace companies use some version of FMECA. FMECA is the standard to good design in rocket structure analysis. It’s a reliability procedure to identify possible failure points in a rocket.

In other words, every component and system of a rocket goes under the microscope. The goal is to calculate the fault tolerance of these components and systems.

Fault tolerance: think of it as a function of three main parts. For a rocket, the parts include the following:

  • Vehicle integrity
  • Mission success
  • Crew safety

Then, you need to answer the following types of questions:

  • If a component fails, how likely is it the mission will succeed?
  • If a component fails and the rocket goes unharmed, will the crew remain safe?

So a component with high fault tolerance will have a high probability of failure. This then becomes a big concern, because if the component fails, the rocket will explode. As a result, this component receives the highest level of criticality.

Important note: Critical Items List (CIL) items go through the following checks: 

  • Rigorous analysis
  • Quality control
  • Manufacturing improvement processing
  • Constant maintenance servicing 

#2 Factor of Safety (FoS) margins

FoS is the safety factor used in structural analysis. It tells you how much stronger a structure is than required for a given load. And FoS values for different structures are typically found in various codes and standards.

To point out, the FoS calculation isn’t an exact science. Especially for large and complex projects. But, engineers do their best to calculate the FoS to a reasonable accuracy. Also, they use past failure data to support their calculations.

I find the FoS is proportional to your level of uncertainty over a design. What I mean is, the better you can predict your load and materials, the less you’ll rely on an FoS. So, loads are arbitrarily increased when an engineer is unsure of the max load. This in return increases the FoS.

With rockets though, it’s always preferred to use a low FoS. As a result, the structural analysis becomes more rigorous as there’s no room for error. 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

Rocket components ride a fine line between working and failing. And the driving reason is a rocket’s weight.

In 2008,  NASA said it costs $10,000 to put 1-pound of payload into Earth’s orbit. Not surprisingly, it’s in everyone’s financial interest to keep a rocket’s weight down. For this reason alone, NASA typically uses a 1.25 FoS for expendable launch vehicles. So, these NASA rockets will fail at 1.25 times the design load.

What’s more, when you go from an FoS of 2 to 1.5, you can cut back on up to 1,000 pounds of weight. This calculates to a savings of 10,000,000. To point out though, with humans on board, the FoS can only go so low. <div class="bg"> <div class="Image"><img src="https://engineercalcs.com/wp-content/uploads/2020/09/Blue-Bulb-Size-3.jpg" width="60px" /></div> <div class="Text">  <span style="color: #3a3a3a;"><strong>Important note:</strong> </span><em>SpaceX's "reusable rockets" are not completely reusable. Certain components need replacement after around 10 or so flights. </em><em>Then, other components need weeks of service after every launch. Without this touch-up work, the designed FoS would dip a lot. </em>  <em><a href="https://www.spacex.com/about/capabilities"><strong>SpaceX's Falcon Heavy</strong></a> advertises $3,100 per pound to orbit. So as technology further advances, this cost will continue to drop.</em>  </div> </div>  [caption id="attachment_3048" align="alignnone" width="900"]<img class="wp-image-3048 size-full" src="https://engineercalcs.com/wp-content/uploads/2020/05/first-launch-of-the-spacex-falcon-heavy-rocket.jpg" alt="first launch of the spacex falcon heavy rocket" width="900" height="600" /> The first launch of the SpaceX Falcon Heavy rocket (Photo Credit: <a href="https://unsplash.com/@billjelen">Bill Jelen</a>)[/caption] <h2><strong>#3 Rocket load analysis</strong></h2> Load analysis is another critical part of rocket design. There are 3 critical tests engineers do to ensure a rocket will successfully complete its mission. <h4><strong>1) Thermal gradient testing</strong></h4> Testing the internal and external skin of a rocket. This checks the effects of thermal gradients a rocket experiences in a launch. These temperatures are both unworldly hot and cold. <h4><strong>2) Pressure testing</strong></h4> Checking internal and external strains on a rocket's frame due to pressure variances. Engineers do repeated depressurizations and re-pressurizations to simulate a liftoff. Also to simulate the entry into space and the return into Earth's dense atmosphere. <h4><strong>3) Load testing</strong></h4> Testing at the designed load and max expected load. The rocket load sources include the following: <ul>  	<li>Aerodynamic drag loads</li>  	<li>Ambient temperature</li>  	<li>Engine vibrations</li>  	<li>Gimbaled thrust</li>  	<li>Rocket acceleration</li>  	<li>Thermal expansion, both transient and steady-state</li>  	<li>Transient dynamic loads</li> </ul> With a gimbaled thrust system, you can generate nonuniform thrust. This is when the exhaust nozzle of a rocket swivels from side to side relative to the rocket's center of gravity. Then with transient dynamic loads, you can have thrust asymmetric flow. This happens when the many engines of a rocket don't fire uniformly. So there's A LOT to consider.  Even more, engineers run extra tests when a component meets any one of the following criteria: <ul>  	<li>A component has a high criticality of failure.</li>  	<li>Any previous analysis leads to uncertainty.</li>  	<li>The minimum set fatigue margin isn't met. We look for how long a component will last after repeated use before issues come up.</li> </ul> A lot of the time too, with each test, load levels are incrementally increased until failure. This helps determine physical limits and critical items in a rocket's design. <h2><strong>#4 Rocket material selection</strong></h2> [caption id="attachment_3045" align="alignnone" width="603"]<img class="wp-image-3045 size-full" src="https://engineercalcs.com/wp-content/uploads/2020/05/the-space-shuttle-discovery-and-its-seven-member-STS-120-crew.jpg" alt="the space shuttle discovery and its seven member STS-120 crew" width="603" height="924" /> The space shuttle Discovery launch with its seven-member STS-120 crew (Photo Credit: <a href="https://spaceflight.nasa.gov/gallery/images/shuttle/sts-120/html/sts120-s-028.html">NASA</a>)[/caption]  At the most basic level, a rocket's structure creates 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 the following: <ul>  	<li>Propellant</li>  	<li>Payload</li>  	<li>Humans</li> </ul> Not surprisingly, selecting the right rocket frame material is a tall order. Just look at this long list of challenging requirements: <ul>  	<li>Sustain high forces during max aerodynamic pressure in launch and ascent.</li>  	<li>Withstand very low temperatures in a rocket's liquid fuel systems. With cryogenic propellants like liquid hydrogen, temperatures reach <strong><a href="https://blogs.nasa.gov/Rocketology/tag/liquid-hydrogen/">-253°C or -423°F</a></strong>.</li>  	<li>Withstand extreme high temperatures in a rocket's combustion chamber and exhaust area. Temperatures reach as high as <strong><a href="https://www.nasa.gov/vision/earth/technologies/13apr_gradient.html">2,760°C or 5,000°F</a>.</strong> Even more, methane engines can reach temperatures near 6,000°F. The temperature of the surface of the sun is <strong><a href="https://www.jpl.nasa.gov/nmp/st5/SCIENCE/sun.html">10,000°F</a></strong>.</li>  	<li>Tolerate hydrogen embrittlement with the usage of hydrogen propellant.</li>  	<li>Remain lightweight to limit the required amount of propellant.</li>  	<li>Strong enough to carry max load, while not buckling from launch and ascent stress.</li> </ul> <h3><strong>Material selection specifications</strong></h3> The goal is to use a material with the following properties: <ul>  	<li>Certain stiffness</li>  	<li>High strength</li>  	<li>Resilient to extreme temperatures</li>  	<li>Lightweight</li>  	<li>Cost-effective</li> </ul> The choice of materials is currently limited to the following: <ul>  	<li>Aerospace-grade aluminum</li>  	<li>Aerospace-grade titanium</li>  	<li>Stainless steel 301 (Elon Musk's material of choice for SpaceX's Starship rocket)</li> </ul> These are all high-density metals you can make very thin without losing out on strength. And to further highlight their advantages, let's touch on other materials: <ul>  	<li>Low-density metals compared to high-density metals have a lower melting point.</li>  	<li>Low-density metals have a high chemical reactivity. This makes them unsuitable for all phases of propellant usage. They can't tolerate contact with cryogenic fuels and hot exhaust gases.</li>  	<li>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 forces in a launch.</li> </ul> <h2><strong>#5 Rocket mass ratio</strong></h2> A critical rocket design element is the mass ratio. This is the ratio of fuel carried by a rocket to the mass of the rocket itself.  With a greater mass ratio, a rocket will have a greater change in velocity (delta-v). To illustrate, to reach Low Earth Orbit (LEO), a rocket needs to travel <strong><a href="http://www.spaceacademy.net.au/watch/track/leopars.htm">7.8 km/sec</a></strong>. So from a standstill on a launchpad, a rocket needs a delta-v of roughly 10 km/sec. And we use 10 km/sec versus 7.8 km/sec because we need to consider the force of drag and gravity on the rocket.  Knowing this, we can use Tsiolovsky's rocket equation to do a mass ratio calculation. <h3><strong>Tsiolkovsky rocket equation</strong></h3> This equation relates the max change of a rocket's speed with no external forces applied. The equation considers the following critical variables: <ul>  	<li>Exhaust velocity from a rocket's nozzle. A rocket expels gas at a certain rate to create the energy to propel upwards.</li>  	<li>The initial and final mass of a rocket.</li> </ul>\Delta v = \lvert v_{e}\rvert ln(\dfrac{m_{o}}{m_{f}})\dfrac{\Delta v}{\lvert v_{e}\rvert} = ln(\dfrac{m_{o}}{m_{f}}) \Rightarrow e^{\dfrac{\Delta v}{\lvert v_{e}\rvert}} = e^{ln(\dfrac{m_{o}}{m_{f}})}Where, \Delta v= delta-vm_{o}= initial total mass of a rocket (includes rocket propellant)m_{f}= final total mass of a rocket (without rocket propellant)v_e= ejection speed of exhaust gases out of a rocket's nozzle Next, let's discuss our equation inputs: <ul>  	<li>To reach LEO, an object needs to travel to an altitude of 200 km while traveling 7.8 km/sec.</li>  	<li>Delta-v needs to be between 9 to 10 km/sec. As previously 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.</li>  	<li>Exhaust velocity depends on the chemical propulsion system selected. For example, a kerosene-oxygen mix produces an exhaust velocity of 3.1 km/sec. Whereas a hydrogen-oxygen mix produces an exhaust velocity of 3.4 km/sec. We'll use 3.4 km/sec.</li> </ul>\Rightarrow \dfrac{m_{o}}{m_{f}} = e^{\dfrac{9,900}{3,400}} = e^{2.91} = 18.36Now, we calculate the percentage of rocket mass, which is fuel:1 – 18.36^{-1} = 94.55%. So pretty much, astronauts are onboard one huge missile. <h3><strong>The fuel weight ratio of NASA's Saturn V Rocket</strong></h3> Let's look at NASA's famous Saturn V rocket for a real-world example. 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 and 318,000 gallons of liquid oxygen for combustion. In total, the Saturn V rocket was<strong> <a href="https://www.nasa.gov/mission_pages/station/expeditions/expedition30/tryanny.html">85% fuel</a></strong>. Crazy, right?!  Even crazier is how a regular 12 oz soda can is 94% soda, while a NASA shuttle external tank is 96% fuel. Pretty amazing given you drink from one can, while the other we launch into space. <h3><strong>Rocket speed versus rocket mass </strong></h3> Rocket speed heavily relies on rocket mass. To illustrate, we'll focus onm_{f}, while again using the Tsiolkovsky rocket equation. With a rocket at rest, the change in velocity, delta-v, becomes the final velocity as shown below.\Delta v = \lvert v_{e}\rvert ln(\dfrac{m_{o}}{m_{f}})<div class="bg"> <div class="Image"><img src="https://engineercalcs.com/wp-content/uploads/2020/09/Blue-Bulb-Size-3.jpg" width="60px" /></div> <div class="Text">  <span style="color: #3a3a3a;"><strong>Important Note:</strong> </span><em>this equation as setup doesn't consider air resistance and gravity in a rocket's launch and ascent.</em>  </div> </div> To point out,m_{f}is the mass of a rocket without propellant. So as them_{f}value increases, the natural log ratio ofm_{0}tom_{f}decreases. This is assumingm_{o}is constant. In return, delta-v drops.  To combat this issue, we increase the propellant to keep the ratio ofm_{o}tom_{f}in check. Without this increase in the propellant, we wouldn't achieve the delta-v required to enter LEO. And this is why you keep the rocket weight as low as possible. Because the cost can grow fast as you add more propellant. <h2><strong>#6 Rocket geometry</strong></h2> The structure of every rocket you see is long, thin, and tube-shaped. And what's amazing is, part of this design is nature-inspired.  Think of a rocket's nose cone. It's one of the strongest architectural shapes you can find in nature. <h3><strong>Rocket's nose cone and the unbreakable egg</strong></h3> Now, think of the eggs you eat for breakfast. Imagine squeezing an egg between two of your hands, along the egg's long axis.  To the surprise of many, it's near impossible to break the egg. And the secret is the egg's curvature without having any angles. So as you place an even force on the egg's domes, the force spreads out. The force then travels down the sides of the domes distributing evenly preventing cracking.  This is why a rocket's nose cone has the shape of an egg. It can better pierce the atmosphere at supersonic speeds without cracking. <h3><strong>Rocket's small diameter frame</strong></h3> A small diameter frame helps a rocket reach supersonic speeds. Just think of how an arrow cuts through high winds with ease. The larger the arrow diameter is though, the greater drag it'll experience. This is because it'll need to push more air out of the way to travel.  To point out, drag relates to the cross-sectional area of an object as it pushes through the air. So, the thinner an arrow is, the less drag it'll experience. The same concept applies to rockets.  For fun, shoot an arrow with an umbrella attached to the end. I'm sure you can guess the outcome. <h3><strong>Rocket equation for drag</strong></h3> Let's look over the math for drag now:D = \dfrac{C_{d} \times A \times \rho \times V^{2}}{2}Where, D= drag forceC_{d}= drag coefficientA= cross-sectional area of a rocket's front nose cone\rho= density of fluid (air)V= speed of a rocket relative to air A flat plate object will have aC_{d}of 1.28, while a nose cone object will have aC_{d}of 0.295. Of course, assuming both objects have the same frontal surface area.  Knowing this, asAincreases,Dincreases too. So, to keepDminimal, we need to keepAas small as possible. <div class="bg"> <div class="Image"><img src="https://engineercalcs.com/wp-content/uploads/2020/09/Blue-Bulb-Size-3.jpg" width="60px" /></div> <div class="Text">  <span style="color: #3a3a3a;"><strong>Important note:</strong></span> <em>the drag coefficient is commonly calculated experimentally. The experiment happens inside a wind tunnel supported with computational fluid dynamics analysis. </em><em>So,C_{d}is a complex value with many variables in its function. You need to consider the effects of air viscosity, compressibility, and so much more.</em>  </div> </div> As one step further, let's look at theVvariable in our above equation. You can see how air drag increases with the square of your speed. And this leads us to something very cool.  If a rocket accelerates too quickly, it'll burn too much fuel just to maintain a constant speed. So, rockets accelerate slowly after launch when drag is the greatest. Then, as the air gets thinner at higher elevations, the rocket speeds up. This saves a lot of fuel. <h2><strong>#7 Rocket thrust</strong></h2> [caption id="attachment_3047" align="alignnone" width="616"]<img class="wp-image-3047 size-full" src="https://engineercalcs.com/wp-content/uploads/2020/05/spacex-falcon-heavy-rocket-ascends.jpg" alt="spacex falcon heavy rocket ascends" width="616" height="924" /> SpaceX Falcon Heavy rocket ascends (Photo Credit: <a href="https://unsplash.com/@billjelen">Bill Jelen</a>)[/caption]  Thrust is the force, which moves a rocket through air and space. And we already learned a rocket needs to travel very fast to reach orbital velocity. So the more thrust the better. And to point out, thrust depends on the following variables: <ul>  	<li>The amount and speed of gas, a rocket's exhaust nozzle fires out</li>  	<li>The shape of a rocket's exhaust nozzle, where the gas exits</li> </ul> At the same time, the thrust force needs to be greater than a rocket's weight. Because the thrust force must overcome the force of gravity, which pulls a rocket down.  Even more, the thrust force must overcome air resistance. 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 so critical as we discussed in the previous section. <h3><strong>Rocket equation for thrust</strong></h3> First, we'll rearrange an equation we previously used. We'll solve forv_{e}.\lvert v_{e}\rvert = (\Delta v) ln(\dfrac{m_{o}}{m_{f}})Asm_{f}increases,v_{e}decreases given all other variables remain constant. This tells us heavier rockets require greater exhaust velocity. And now, we can calculate rocket thrust.F = m_{dot}v_{e} + (p_{e} – p_{0})A_{e}Where, F = amount of thrust produced by a rocketm_{dot}= the rate of ejected mass flow (the amount of gas passing through a rocket's nozzle per unit of time)v_{e}= ejection speed of exhaust gases out of a rocket's nozzlep_{e}= pressure of exhaust gasesp_{0}= pressure of ambient atmosphereA_{e}= the area ratio of a rocket's nozzle's throat to exit (a rocket's throat is the smallest cross-sectional area of the nozzle) Looking at both equations together now,v_{e}andFdecrease with heavier rocket frames. So a rocket won't reach orbit with all else constant, as its mass increases. <h3><strong>How to increase thrust with heavier rockets?</strong></h3> The two most obvious answers won't work. Let's quickly discuss them.  <strong>#1 IncreaseA_{e}</strong> You can't infinitely make a rocket's nozzle exit larger. For one, you'll add weight to the rocket. But also, the area ratio between the nozzle's throat to exit is already finely designed. There's a fine balance betweenA_{e}and the stored fuel quantity. Even more, engineers have considered almost all design options using today's technology. This includes the design ofA_{e}against the max rocket weight. So you can't double the max payload and think adjustingA_{e}alone will get you into orbit. <strong>#2 Increasem_{dot}</strong> m_{dot}is a function of the engine and chemicals used. Assuming the nozzle size remains constant. The issue is, we've investigated near all chemical propulsion systems. So more than likely we can't increasem_{dot}with the chemicals used today. Even as rocket engines become more efficient, the rate of ejected mass flow won't change much. So, what's left? We either wait for nuclear propulsion to become a viable tech, or we increase the propellant. In the end, the answer seems to always be more propellant. And to summarize, a heavier rocket today needs the following to enter LEO: <ol>  	<li>More propellant</li>  	<li>Propellant exiting faster from a rocket's nozzle</li>  	<li>A combination of 1 and 2</li> </ol> <div class="bg"> <div class="Image"><img src="https://engineercalcs.com/wp-content/uploads/2020/09/Blue-Bulb-Size-3.jpg" width="60px" /></div> <div class="Text">  <span style="color: #3a3a3a;"><strong>Important Note:</strong></span><em> 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. </em>  </div> </div> <h2><strong>#8 Important rocket design considerations</strong></h2> Let's dive deeper into even more rocket design considerations. This will further show the complexity of designing a rocket. <h3><strong>Axial force and bending moment</strong></h3> 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 travel straight up, it has a tilt. This steering technique allows a rocket to preserve fuel. But also, reduces stress and strain on the frame.  The tilting brings its own problems though. The tilt causes an axial force and bending moment. More specifically, a rocket's thrust, drag, and weight generate the axial force. While the rocket traveling at an angle creates the bending moment. <div class="bg"> <div class="Image"><img src="https://engineercalcs.com/wp-content/uploads/2020/09/Blue-Bulb-Size-3.jpg" width="60px" /></div> <div class="Text">  <span style="color: #3a3a3a;"><strong>Important Note:</strong> </span><em>the bending moment force compresses one side of the rocket. But also, causes tension on the opposing side. Just think of what happens when you bend a drinking straw.</em>  </div> </div> To better understand the forces, let's view the complete line load equation for a rocket. <h4><strong>Complete line load equation</strong></h4>N_{t} = \dfrac{F_{x}}{2\pi R}+(p\dfrac{R}{2}+\dfrac{M}{\pi R^{2}})F_{s}Where, N_{t}= ultimate tensile line loadF_{x}= axial forceF_{s}= shear force M = moment R = rocket radius Looking at the equation, asF_{x}andMincrease,N_{t}$ increases. So, the below rocket design elements need consideration against the forces. Otherwise, a rocket will buckle as it ascends.

  • Frame material
  • Rocket wall thickness
  • Rocket shape

Vibration loading

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 violent vibrations. You can measure these vibrations on the vertical axis of a rocket.

The source of the vibrations is instability in the structure and the propulsion system. The flow of propellant feeding the engines causes what’s called thrust oscillation.

To tackle this problem, NASA first began using accumulators with their engines. This helped suppress the vibrations. But, there are also vibrations in the liftoff stage from rocket engine noises. The emission of hot gases breaks the sound barrier causing shockwaves. And this isn’t a surprise, considering a rocket produces a thrust of 7.5 million-plus pounds in a launch.

Fracture control

In structural work, all parts will have flaws to some degree. Think of crack-like defects. And as you’d guess, the growth of cracks will over time compromise the integrity of a structure.

Think of an old building with an eroded foundation. This wouldn’t be a building you’d want to call home. In rocket structure analysis, the same concept applies. In fact, structural integrity becomes an even greater concern with rockets.

This is why fracture control is critical in controlling the effects of structural flaws in rockets. So, space programs test in different extreme environments to find weaknesses. For example, will a propagated crack lead to mission failure in extreme heat?…

Rocket structure analysis wrap up

A rocket is a boring-looking metallic tube fired into space. Yet, rockets are some of the most complex man-made machines. It’s an understatement to say a lot goes into rocket design. In fact, rocket design requires the use of almost every type of engineering. The structural side is only one part.

So the amount of thought and effort to make a launch possible is mind-blowing. Even more amazing is we as a society are only scratching the surface of what’s possible with rockets. And as the price of launches drops and rockets become safer, we’ll set foot in a new age of space exploration. It’s an exciting time to be alive.

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)

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