MAGLEV Contest

In determining the feasibility of a real MAGLEV transportation system, performance will be based upon speed, vehicle cost, and passenger capacity, among other factors. Awards will be distributed based on these and other performance categories.

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A Real MAGLEV Must Meet Several Criteria at Once

• It should go as fast as possible. The faster you make trips between any two points, the faster you collect fares - that is, make money.
• It should carry as many passengers as possible. Since each passenger pays a fare, the more passengers you carry per trip, the more money you make.
• It should be as cheap as possible. The cheaper the vehicle, the fewer trips will be needed for you to pay back the vehicle's cost and start making a profit. If the vehicle is too expensive, the number of trips you would need to pay it off may even turn out to be greater than the number of trips it can actually make before it wears out. So, you'd never get your money back, let alone make a profit.
• Other factors are also considered, such as operating and maintenance costs, how long the vehicle actually lasts, the route chosen, the number of people who might want to travel this route, reliability, public confidence and availability of financial support, etc.. However, to keep things simple while illustrating basic engineering principles, in the MAGLEV contest we confine ourselves to speed, number of passengers, and cost.

There Will Be Tradeoffs Between Design Requirements

All else being equal, adding passengers will tend to reduce a vehicle's maximum speed. Passengers add weight. They also make the vehicle larger. Pennies will be used to represent passengers carried by a model vehicle.

All things being equal, increasing a vehicle's carrying capacity will tend to increase cost. A heavy-duty MAGLEV suspension system to support a larger car and the more people will probably cost more than a light-duty system. Vehicle costs will be represented by the number of magnets used in a model vehicle.

The Design Engineer Must Find the "BEST" Tradeoff

The engineer must design a vehicle which carries the most pennies at the fastest speed while using the least amount of magnets. This is how real engineering problems present themselves. The engineer who finds the best compromise is the one who becomes successful.

The engineer will need some way to actually judge which compromise is best. Is a car which goes twice as fast, has half as many magnets and half as many pennies as another car "better" or "worse"?

A Way is Needed to Compare These Tradeoffs

• Comparisons are often made in practice by defining a Figure of Merit (FOM)for the design problem
• The FOM is simply a mathematical way of assigning a single number to each different compromise of the things you're looking at - in this case, speed, number of passengers (pennies), and cost (number of magnets). This is done in such a way that "better" compromises have higher FOM's.
• Example: Suppose you're designing a bridge. You want it to be strong, but also light. If don't care about weight, you can make a bridge as strong as you want by adding beams to it. If you don't care about strength you can make a bridge as light as you like by making beams thinner and thinner.
• But how to judge how well you did in keeping weight low and strength high? You want a FOM that will increase when strength increases, and decrease when weight increases. Here, a simple math expression that has these properties is the strength-to-weight ratio:
  FOM (bridge) = strength/weight
• In BNL's Model Bridge Contest, a bridge is weighed. Its strength is determined by loading it until it breaks. By this FOM , a bridge that holds 25Kg and weighs 10g (FOM of 2500) is a better design than one which holds 50 Kg but weighs 50g (FOM of 1000).

Ratio performance measures of this sort are very common: price-to-earnings ratio for stocks; miles-per-gallon for cars; price-per-pound for meat, etc. By using them we can compare Apple with IBM, Volkswagens with Hummers, and sirloin with hamburger. Similarly, we can construct an FOM to compare maglev designs with different speeds, capacity and cost:

• Let S stand for measured speed. All else being equal, we want the FOM to be greater for vehicles with greater speeds. So, we'll make the FOM directly proportional to S.
• Let P stand for the number of pennies carried, representing passengers. All else being equal, we want the FOM to be greater for vehicles carrying more passengers. So, we'll also make the FOM directly proportional to P
• Let N stand for the number of magnets in the vehicle's suspension, each of which adds the same amount to vehicle's cost. All else being equal, we would like the FOM to be smaller for vehicles needing a greater number of magnets. So, we'll make the FOM inversely proportional to N.
• All three statements can be simultaneously expressed in a simple algebraic relation:

  

  This can be put in terms of what we will measure. Let the distance between timing points on the track be "X" feet. Let the time to go between the timing points be "T" seconds. Speed (S) = X/T. That gives you (algebra):

  

For the MAGLEV contest, P, and/or N and/or T may be different for each vehicle. X however will be the same for all vehicles, i.e. the 16' between the timers. To get the FOM, multiply the number of pennies (P) by 16' (X) and divide the result by the number of magnets (N) and again by the measured time (T, in seconds).