The movie Top Gun starring Tom Cruise made jets and aircraft carriers iconic. So, let’s go through the calculations of an F-14 Tomcat carrier launch.
These launches are marvels of engineering. Massive jets taking off and landing on floating airports.
The ocean’s airports
The USS Theodore Roosevelt is a nuclear-powered aircraft carrier. It stands 20 stories above the ocean.
Also, it’s 1,092-feet long with a 196,000 square-foot flight deck.
This monster-sized ship houses 80 plus aircraft. Then around 6,000 people call the ship home for several months.
It’s an understatement to say it’s huge! But still, how do fighter jets take off from these floating airports?
To answer this question, we need to first go over how planes take off.
The science behind the takeoff of planes
Planes need to get enough air under their wings to generate lift. How does this happen?
Plane wings have a unique shape that makes air move faster over them.
Bernoulli’s principle states fluids that move faster than their surroundings have less pressure. Our fluid is air.
So, the goal is to create less pressure on top of the wings than below by going fast. This pressure difference creates a force on the wings that lifts the wings up into the air.
To help planes pull this off, aircraft carriers offer two things not found on land airports.
#1 Catapult system
The typical aircraft runway is 2,300 feet long. While an aircraft carrier has a runway of only around 300 feet.
2,000 feet is a lot of aircraft runway to give up. This means planes have less runway to gain speed for takeoff.
To compensate for this, aircraft carriers use steam-powered catapults. These catapults launch aircraft from 0 to 170 miles per hour in 2 seconds.
This creates the force required to push an aircraft forward to gain enough speed to create lift.
Important to realize, every plane model differs in some way. The differences include:
- Aerodynamic shape
- Engine output
For this reason, the catapult operator sets the pressure according to each plane. The settings are far from simple though.
- Set pressure too low: a plane won’t move fast enough. As a result, the catapult will shoot the plane into the ocean.
- Set pressure too high: the sudden jerk could break a plane’s nose gear.
#2 Ocean assistance
Aircraft carriers move fast in oceans cutting through the air. As a result, this can create additional airflow on the flight deck.
This additional airflow helps when you travel in the direction of a jet’s takeoff. Thus, a jet’s minimum takeoff speed would decrease.
Remember, the goal is to make air move faster over a plane’s wings.
Catapult system speed calculation
With each launch, operators need to figure out the catapult system’s settings.
An operator determines these settings by the specific plane type as we just learned. But, operators also make other considerations as well, which include:
- Wind speed across the aircraft carrier deck
- Air density
- Speed of the aircraft carrier
Important Note: launching into the wind, the catapult needs to create greater pressure. Because the wind is reducing the jet’s speed.
Now, I’m going to simplify our calculation and not consider these other variables. We can still make a fairly accurate calculation though.
So, let’s now dig our feet into an F-14 Tomcat carrier launch. The F-14 Tomcat was Maverick’s (Tom Cruise’s) fighter jet of choice.
This amazing jet can sweep its wings backward and forward.
- In-flight to go high speed, a pilot sweeps the wings back. This creates a more aerodynamic shape.
- For takeoff and landing, a pilot sweeps the wings open. This maximizes the surface area of the wings. We’ll learn why this is so important, especially when an aircraft carrier is the airport.
Important Note: this sounds and looks very cool. But, the swing-wing design was a maintenance nightmare.
When you have many moving parts, you create more points of failure. Plus, this system added a lot of weight to the jet.
How fast will the catapult shuttle need to travel to launch an F-14 Tomcat?
According to the Aerospace Web, the max takeoff weight of an F-14 Tomcat is 74,350-pounds (33,725 kilograms). With this information, we can start our calculation.
We’ll use the lift formula:
= lift force in pounds or newtons. The weight of the F-14 Tomcat.
= lift coefficient. In our case, the max takeoff lift coefficient.
= density of air in the takeoff region. At sea level, is 0.0023769
= true airspeed. How fast the aircraft travels.
= surface area of the wings. The F-14 Tomcat wing area is . This is the wing area when the wings are fully forward.
Important Note: the value is normally determined through experiments. It considers the shape, inclinations, material density, and flow conditions of a wing.
This value will tell us the performance of airfoils and wings when it comes to lift. In other words, how well a plane can take off.
Using Haw Hamburg, the takeoff lift coefficient for a fighter jet is between 1.4 to 2.0. This value comes from Dr. Jan Roskam’s amazing Airplane Design books.
In our calculation, we’ll assume a of 1.4.
Also, for the F-14 Tomcat to takeoff, the lift must overcome gravity and equal the weight of the jet. That said, let’s now plug in our values and solve for .
The lift equation tells us the higher the lift coefficient is, the slower a plane needs to travel to take off. Keep in mind, it’s much safer to fly as slow as possible in takeoff.
This is why a high aspect ratio wing is desirable. This becomes even more important for planes on aircraft carriers.
I’ll explain this in greater detail when I discuss .
Catapult system speed mistake calculation
Humans make errors. So, what would happen if the catapult system was set to the wrong speed?
Let’s say 0.9v, where ‘v’ is the catapult speed.
We’re going to use our previously calculated F-14 Tomcat values to answer this question. But, we’ll also use the thrust for the two jet engines in our calculation too.
- The thrust of the F-14A engines is 30,570 lbs (136,000 Newtons)
- The thrust of the F-14A engines with afterburners is 41,800 lbs (185,940 Newtons)
To make this calculation, we’ll assume the following:
- F-14 Tomcat will not use its afterburners
- Aircraft carrier deck for liftoff is 60-feet (18.29 meters) above water
- F-14 Tomcat will leave the edge of the runway traveling horizontally
First, we calculate how much lift we produce. We substitute 0.9v into our lift equation.
Once the F-14 Tomcat takes off, the lift on the aircraft is:
What does this 90.00% mean? The jet is falling with an acceleration of 10.00% of gravity.
Where acceleration due to gravity is
We now solve for the time it takes for the jet to fall 60 feet. This is the height of the aircraft carrier.
Important Note: we ignore the increase in horizontal velocity for the few seconds after launch. This increase in velocity does create more lift. But, our calculation would then become a calculus problem.
Now, we will calculate the amount of trust the jet needs to generate to accelerate from 0.9v to v in 6.10 seconds.
First, we calculate the jet’s acceleration: , where
Next, we calculate the jet’s thrust,
Mass of F-14 Tomcat =
This required engine thrust is less than the F-14 Tomcat’s full thrust. So, even with the catapult speed mistake the jet will still safely takeoff.
Having this wiggle room makes for safer takeoffs.
Lift factors: manufacturer versus pilot controlled
Now that we’ve gone over the lift equation, let’s look more closely at the lift variables.
I’m going to summarize concepts here. In other words, cram a lot of complex aerodynamics into simple words.
This will allow us to see how much control a pilot has in creating lift.
: the aircraft manufacturer determines the surface area of the wings. The pilot has no control over this.
: air density is dependent on a plane’s altitude. The higher a plane flys, the less dense the air becomes.
So, given certain flight conditions, becomes constant. A pilot can’t do anything to change the air density.
: true airspeed the pilot controls. To be more precise, we call it Indicating Air Speed (IAS).
So, the dynamic pressure, , is viewed as IAS by the pilot.
: the aircraft manufacturer controls most parts of this dimensionless figure. This figure highly depends on the following factors:
- Camber of the airfoil
- The shape of the planform
- The Angle of Attack (AOA)
I’ve illustrated these 3 factors in the image below.
Which lift coefficient factors can pilots control?
The pilot can only control the AOA.
The AOA is the angle between oncoming air or relative wind and a set assumed line on the airplane. So by controlling the pitch of a plane, AOA, the lift changes.
That said, if AOA changes and we adjust speed accordingly, the lift may not change. Rather, the aircraft can maintain level flight. The lift coefficient will change though.
Lift Coefficient vs Angle of Attack
Let’s now better understand the direct relationship between the lift coefficient and AOA. We’ll start by reviewing the below graph.
I understand I’ve overly simplified the concepts. But, the graph will still help to show the interdependencies of aircraft design when it comes to lift.
So, to increase , you increase AOA.
But, increase AOA too much and the plane will stall. Then lift decreases. This is where you see the curve start to go downwards in the graph.
Every plane will have a different lift coefficient versus AOA graph. That said, the graph depends on the following:
- The shape and size of the wings
- The curvature of the lead edge of the airfoil
What’s the takeaway with all these lift variables?
The aircraft manufacturer controls many parts of lift. While the pilot has some control too.
All in all, plane takeoffs are very complex. Many interrelationships exist between the variables we’ve discussed.
For example, if I only tell you I increased the pitch of an aircraft by 5 degrees, you won’t know how AOA impacts lift.
Maybe I lowered my airspeed to keep a constant altitude as I increased AOA.
The F-14 Tomcat forever lives in pop culture because of the Hollywood movie Top Gun. I remember wanting to become a fighter pilot as a kid because of this movie.
Many years later, I found out the F-14 Tomcat had many shortcomings. For one, the jet was designed before computer-aided design assistance existed. So, it had aerodynamic flaws.
Despite the shortcomings, it was still an amazing feat of engineering for its time. Plus, it looks badass.
To this day, I’m amazed by how machinery this heavy takes off on such short 300-foot runways.
What do you find most fascinating about an F-14 tomcat carrier launch? What part of the engineering with an F-14 Tomcat carrier launch do you think is most critical?
Featured Image Photo Credit: U.S. Navy via Photographer’s Mate 3rd Class Todd Frantom (image cropped)
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Koosha started Engineer Calcs in 2020 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.