What is the terminal velocity of a Tyrannosaurus Rex?

This is a great thought experiment to challenge young designers and engineers.  How would you go about calculating the fastest speed at which a Tyrannosaurus Rex could fall? 

To get started, one must first understand the concept behind terminal velocity.  When an object is falling, it has two forces acting on it: the pull of gravity and the friction of air pushing back.  Earth's gravity (g) pulls objects at an acceleration rate of 9.8m/s^2.  An object will keep accelerating until the friction of air slows down the acceleration to a stable velocity, or terminal velocity. 

There is a bit more going on to figure out the terminal velocity of a Tyrannosaurus Rex.  This is a balance between the mass (m) of the object and the surface area (A) of the object through a certain density of air (p) as well as the drag coefficient of the object as it moves through the air (Cd).

The mass (m) of a T-Rex ranges from _ to 5,500 kg for an adult.  We'll go with the most terrifying at 5,500 kg

The gravitational constant (g) only changes if you go off-planet.  We'll stay on Earth today to not get too crazy at 9.8m/s^2.

We'll also assume that the T-Rex can reach terminal velocity by the time it reaches 2200km altitude, which has a pressure of 0.99 kg/m^3.

We then have to make a decision whether the T-Rex is falling in a streamlined nose-firstor simply an uncontrolled sideways fall.  Let's go for speed and say that the drag coefficient is really low at 0.7 and that the area (A) of the T-Rex falling is the front skull dimensions of 1.2m^2.

When you drop all of those inputs into the formula, we come to 360 m/s, or 807 mph.  As an aside, the speed of sound is 340 m/s, so a skydiving Tyrannosaurus would be the first animal to generate a sonic boom. 

If you're looking for extra credit, ask your budding young engineers to calculate the size of parachute needed to stop this T-Rex. 

terminal velocity of a tyrannosaurus rex

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