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NAE™ Classroom:
Mathematics Applied to the Physics of Energy, Motion & Force

Dear Students of Science:

The material which follows is an introduction to some basic laws of Physics that apply to the NAE™ and will affect its performance in many ways. Understanding these concepts will develop a greater appreciation for the issues the vehicle will be dealing with as one progresses further along toward the more complex levels of laws. For the first set of lessons, the links below will take you to a site, composed by Professor Tobin of the University of Hawaii. They will explain, in simple terms, the first three laws of Physics.

Newton's Three Laws of Physics 

Now that we have an understanding of the basics of calculating the force necessary to move an object with a certain amount of weight, let's move on and apply this knowledge to the NAE™ vehicle. The following material is provided by our team scientist, Steve Wallace. Should you have any comments or questions concerning any of the points made here, please contact Jon, the Educational Affairs Director of the team, and he will be happy to respond.

Thrust, Drag, Gravity, or Aerodynamic Loads are all Forces and can be expressed in terms of Newtons in international units, or Pounds(force)or "Lbf" in english units. Pounds(force) and Pounds(mass)are not the same because pounds(force) is Pounds(mass) times acceleration. A bathroom scale measures pounds(force) because it is pounds(mass) times the acceleration due to gravity, otherwise known as "g". On earth, near the equator g = ~1.

In International terms, or "si" units, the mass term is called Kilograms, or thousands of grams. The name for the force term in si units is "Newtons".

F=MA, or Force = Mass multiplied by Acceleration.
Newtons = Kilograms X Meters per Second per Second
or N= Kgm X M/S^2

In english units:
Pounds(force)= Pounds(mass)X acceleration of free fall or "g"
which is close to 1.00 here on Earth.
or Lbf= Lb(mass) X g

1 Pound(Mass) = 0.37324 Kilograms
1 Lbf = 4.4482 Newtons

Our vehicle has a stable net velocity when :
Thrust(Newtons) + Drag(Newtons) = 0
and
Down force(Newtons) + Pressure under the wheels(Newtons) = 0
and
the summation of all Aerodynamic loads (Newtons) = 0

A given Velocity (our GOAL) is expressed in terms of;

Acceleration multiplied by time. Example:
M/sec^2 multiplied by Seconds, which gives you a velocity in Meters per second, which can be converted to Kilometers per hour.

Why do we care about all this information? Because we want to know how fast we can go, and how much distance we need to get up to speed and to slow back down to a stop!

We want to reach 1,287.4751 Km/h, maintain speed for one mile, and stop. This must happen within 12 to 15 miles.

So, to get up to speed, (Mass of vehicle)*(Acceleration)*(Time)*(Friction coefficient)*(wind resistance coefficient) = 1,287Km/hr. We must also be concerned with the power required to make the wheels spin with a rim speed of 800 mph and how we must remove this stored rotational kinetic energy as we brake the car. The task of removing the rotational kinetic energy is accomplished very nicely with our magnetic braking system.

To stop, only the Acceleration term is reversed (we have control over this because we can kill the engine and deploy parachutes to increase air resistance).

We must also consider other limitations such as how fast the vehicle can accelerate while maintaining the safety of the driver and vehicle.

A stable velocity happens when the vehicle is traveling at 800 mph, in a straight line. It also happens when the vehicle is sitting still on the desert floor.

For a really nice site that will give you the capability to choose various factors in an equation, plug in known numbers to the equations used above, and give you answers, go to davidson.com

We invite you to add a comment, or remark, about our program or the site.

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