Gavin's Modeling Project 4

essentially taken from the 1997 MCM

LaSCaM, Inc
Large Scale Management, Inc
8499 Juniper Pond Rd.
SE Lonlinc, SK 07658

20 October 1999

Technical Mathematics, Inc.
Suite 4, Strawmarket Business Plaza
Lonlinc, SK 04685

Dear TMI:

Large Scale Management, Inc., is concerned with acquiring and managing businesses with new and innovative methods to effectively manage and down-size properties. While this has, unfortunately, frequently generated unmerited negative publicity in the press we have selflessly not allowed this to impede our pursuit of higher profit-margins in our relentless march to the proverbial bank. A couple of years ago we acquired what we turned into a very successful game (er---wilderness) park in what has been inappropriately called ``darkest Africa,'' and as the animals therein have mysteriously disappeared, we are exploring its transition into what is tentatively called ``Cretaceous Park,'' for it will next be populated by full-size life-like dinosaur robots. However, to make these life-like, we need to know what life was like in the Cretaceous, and rather than be eaten by dinosaurs we are contacting you to develop a mathematical model of aspects of this environment.

In particular, the velociraptor, Velociraptor mongoliensis, was a predatory dinosaur that lived during the late Cretaceous period, approximately 75 million years ago. Paleontologists think that it was a very tenacious hunter and my have hunted in pairs or larger packs. Unfortunately (?), there is no way to observe its hunting behavior in the wild, as can be done with modern mammalian predators. We need you to help model hunting behavior of the velociraptor. We hope to compare your results with field data reported by biologists studying the behaviors of lions, tigers, and similar predatory animals.

The average adult velociraptor was 3 m long with a hip height of 0.5 m and an approximate mass of 45 kg. It is estimated that the animal could run extremely fast, at speeds of 60 km/hr, for about 15 sec. After the initial burst of speed, the animal needed to stop and recover from a buildup of lactic acid in its muscles.

You are to suppose that the velociraptor preyed on Thescelosaurus neglectus, a herbivorous biped approximately the same size as the velociraptor. A biomechanical analysis of a fossilized thesceloraus indicates that it could run at a speed of about 50 km/hr for long periods of time.

Part 1
Assuming the velociraptor is a solitary hunter, design a mathematical model that describes a hunting strategy for a single velociraptor stalking and chasing a single thescelosaurus as well as the evasive strategy of the prey. Assume that the thesceloraus can always detect the velociraptor when it comes within 15 m, but may detect the predator at even greater ranges (up to 50 m) depending upon the habitat and weather conditions. Additionally, due to its physical structure and strength, the velociraptor has a limited turning radius when running at full speed. This radius is estimated to be three times the animal's hip height. On the other hand, the thescelosaurus is extremely agile and has a turning radius of 0.5 m.

Part 2
Assuming more realistically that the velociraptor hunted in pairs, design a new model that describes a hunting strategy for two velociraptors stalking and chasing a single thescelosaurus as well as the evasive strategy of the prey. Use the other assumptions and limitations given in Part 1.

We look forward to hearing preliminary presentations of your results on the 27th or 29th of this month and final presentations on the 3rd or 5th of November. Your final papers are due the 8th of that month.

Yours sincerely,
Thodore T.U. Rerner
Lord-High CEO, LaSCaM, Inc.

ttur:glr

Gavins Modeling Project 4
Last Modified: Wed Oct 20 10:06:50 CDT 1999
Comments to glarose@umich.edu