# Jurassic Park

## The Movie

Jurassic Park is one of the biggest blockbuster movies of all time, a 1993 movie about a wildlife park of cloned dinosaurs that goes catastrophically wrong. Assuming the core cloning technology was invented, there would be a range of other problems involved in running a dinosaur park, which we’ll get into in this tutorial.

## Math Scenario 1 – Feeding the Park

Many of your dinosaurs are huge, and consequently huge eaters as well! Feeding them is going to be a major challenge, since you have to ship everything in by boat every week.

### Feeding the Carnivores

One of your main feeding concerns is the large carnivores like T-rex.

Your experts calculate that each of your 10 T-rexes needs about 50 kilograms of meat a day. For comparison a lion eats about 5 – 10 kilograms of meat per day.

A standard meat esky contains 100 kilograms of meat.

If the boat comes once per week, calculate how many meat eskies you will need from each boat trip.

*#eskies = #trex × meat per day per trex × #days / meat per esky*

*#eskies = 10 × 50 × 7 / 100*

*#eskies = 35*

### Feeding the Herbivores

You have a much larger number of large herbivores – about 120 sauropods averaging 30 tonnes in size.

Your experts think that each animal will eat about the same amount as a 4 tonne elephant per day, but scaled up to their weight. An elephant eats about 150 kg of vegetation per day.

First we can scale up the amount of food required:

*Food per day per herbivore = food per elephant per day × weight ratio*

*Food per day per herbivore = 150 kg × 30 / 4*

*Food per day per herbivore = 1125 kg*

More than a tonne per animal per day – wow. Now we can calculate how much food the boat needs to bring in each week:

*Herbivore feed required = #herbivores × vegetation per day per herbivore × #days*

*Herbivore feed required = 120 × 1125 × 7*

*Herbivore feed required = 945000 kg*

*Herbivore feed required = 945 tonnes*

## Math Scenario 2 – Fencing

You need to keep the carnivores separated from the herbivores. This requires fencing – and a whole lot of it.

The details for the 6 paddocks shown in the map are as follows:

- 3 circular paddocks with a radius of 500 metres
- 1 large rectangular paddock measuring 500 metres by 1400 metres
- A smaller rectangular T-rex paddock measuring 500 by 650 metres. This paddock has double layers of fencing.
- A triangular paddock with sides measuring 600 metres each

We can calculate the total length of fencing for the circular, rectangular and triangular paddocks:

*Total perimeter = 3 × circle perimeter + rectangle 1 + 2 × rectangle 2 + triangle*

*Total perimeter = 3 × 2 × PI × r + 2 × (L1 + W1) + 2 × 2 × (L2 + W2) + 3 × triangle side length*

*Total perimeter = 3 × 2 × PI × 500 + 2 × (1400 + 500) + 2 × 2 × (650 + 500) + 3 × 600*

*Total perimeter = 9425 + 3800 + 4600 + 1800*

*Total perimeter = 19625 m or 19.625 km*

If the fences have an average height of 10 metres, we can calculate the area of fencing required:

*Fencing area = fencing length × fencing height*

*Fencing area = 19625 × 10*

*Fencing area = 196250 m ^{2}*

## Math Scenario 3 – Pteranodon Cage

The pteranodons are kept in a huge hemispherical cage. The height of the cage at the centre (the radius of the sphere) is 200 metres. We can calculate the area of fencing required to cover the entire hemisphere.

*Hemisphere surface area = half sphere surface area*

*Hemisphere surface area = 0.5 × 4 × PI × r ^{3}*

*Hemisphere surface area = 0.5 × 4 × PI × 200 ^{2}*

*Hemisphere surface area = 251327 m ^{2}*

The pteranodons will need a larger area of fencing material than the rest of the dinosaurs in the park!

## Math Scenario 4 – Outrunning the Velociraptors and the T-Rex

Out on patrol, you get the bad news that the power has gone out and the electric fences are no longer stopping the dinosaurs from mixing. You look up and see an angry T-rex **and** a velociraptor racing towards you. Uh-oh!

Behind you in the distance you see a herd of triceratops – if you can make it to them before getting caught, the herd should give you some protection from the T-rex. You have a stun gun but you don’t want to shoot the carnivores unless there’s no other option. You eyeball the distances to work out whether you have a chance.

- The relative safety of the triceratops herd is 200 metres away. You can get up to a sprint speed of about 25 km/hr straightaway.
- The T-rex is closer, about 100 metres away in the opposite direction. It’s already at top speed, striding towards you at about 35 km/hr.
- The velociraptor is 400 metres away in the opposite direction. It’s sprinting towards you at its top speed of 65 km/hr.

First let’s calculate how long it will take for you to reach the triceratops:

*Time to safety = distance / speed*

*Time to safety = 200 m / (25 km/hr)*

*Time to safety = 200 m / (25 km/hr × 1000 m/km / 3600 s/hr)*

*Time to safety = 28.8 seconds*

To work out whether you’re safe from the T-rex, you can calculate how long it will take to get from its current position to the Triceratops herd. If it’s less than your time, you’re in trouble:

*T-rex time = distance / speed*

*T-rex time = (200 m + 100 m) / (35 km/hr)*

*T-rex time = 300 m / (35 km/hr × 1000 m/km / 3600 s/hr)*

*T-rex time = 30.86 seconds*

The T-rex will get to the herd a couple of seconds after you, so you might be safe from it. What about the raptor?

*Raptor time = distance / speed*

*Raptor time = (200 m + 400 m) / (65 km/hr)*

*Raptor time = 600 m / (65 km/hr × 1000 m/km / 3600 s/hr)*

*Raptor time = 33.23 seconds*

Looks like the raptor will be just behind the T-rex – so you’ve got a chance at safety without having to do anything drastic. Better start running!

## Real-Life Example – How Fast Could Tyrannosaurus Rex Run?

* Chastity / 123rf.com.*

One of the most controversial topics in palaeontology is how fast T-rex could walk or run. Estimates range from 10 or 15 km/hr to 70 km/hr.

One method of estimating speed examines the footprints left by these creatures, along with the estimated length of their legs and models of how two-legged dinosaurs walked or ran.

This approach could give a speed estimate for how fast the dinosaur was moving at that particular point in time… but not necessarily its top speed.

Other methods look at how other animals that are still around today walk and run, like elephants (because they were a similar weight) and birds (because birds are descended from dinosaurs and hence share some similarities).