What constitutes an ideal starting gate?

Several years ago, my son was fortunate enough to go to the district derby. The track used was custom built with a gate that I'm sure one of the dad's had constructed. It didn't take long for me to see the lack of engineering design that went into the construction of that gate. As near as I could tell, it was built with either 3/8” or 1/2” square, solid steel material, and had a fairly hefty spring to pull it open. It was amusing to see the vibration set up when the gate was released, until some of the cars crashed and burned due to the vibration. This, in addition to the experiences with my pack's custom track and gate mechanism, have started me on a quest to build a better gate.

The functions of an ideal starting gate are firstly to hold the cars in place and secondly to provide a smooth, consistent, unobstructed release when the gate mechanism is engaged. The release of the gate also happens to provide a convenient means of triggering the finish line, although it doesn't need to be. More on this later. Mechanisms to hold the cars in place are rather simple; it is the release that actually poses the major mechanical problems.

Ideally, when the release is engaged, the gate should move away from the cars faster than they will move. In a perfect situation, assuming the cars have a coefficient of friction of zero, this would mean that at the point of contact with the cars, the acceleration would be 9.8 m/sec² or 32.2 ft/sec². In reality, this has been an interesting goal to achieve and still maintain a smooth release. The primary factor that we're fighting is what's termed the “moment of inertia” which is defined as an object's resistance to angular acceleration. The moment of inertia for an object, the release gate in this particular instance, is related to the mass of the gate as well as the distance that mass is from the point of rotation.

Newton's laws of motion tell us that the acceleration of an object is proportional to the force exerted and inversely proportional to the mass, and in rotational terms. inversely proportional to the mass and the radius. The basics of the physics that I'm using can be found here and here although any search on angular acceleration will provide the same information. In the above mentioned gate, the force to mass/radius ratio was in line; however the design would be considered a poor one in that the spring imparted one heck of a lot of energy to the gate that had to be absorbed by the track, consequently setting up an undesirable vibration. Yes, you could devise a method of dampening the shock, but using more appropriate materials and adjusting the other variables would eliminate the need for such.

Lets design us a gate just to see how these variables come into play. We're going to design for a 4 lane track with 3.5” centers, with a 1/2” deck thickness. We go to the hardware store and purchase 1” and 1/4” wooden dowels. We'll cut the 1” dowel to 18” (we need a handle to turn it) and the 1/4” dowel to 3 1/4” lengths (1/2” into the 1” dowel which is mounted 3/4” below the deck, 1/2” of deck, and 2” for the cars to rest against). These are probably birch, which has a density of 571 kg/m³, or 35.6 lb/ft³ so the 1”dowel piece would weigh about 0.29 lb and the 1/4” dowels would weigh about 0.012 lb ea (a total of 0.048 lb).

Given a minimum point of contact with the cars at 3/8” above the track and 1 5/8” from the center of rotation, the tangential acceleration at that point should be 32.2 ft/sec² which results in an angular acceleration of the gate of 38 rad/sec². The moment of inertia for one of the pins is 0.079 in²-oz and 0.316 for all four. The 1” dowel has a moment of inertia of 0.58 for a total of 0.896.

The torque required to produce an angular acceleration of 38 rad/sec² is the product of the moment of inertia and the angular acceleration and for the gate we're designing yields 34 in-oz. and if we're providing this torque with a spring attached to the outer circumference of the 1” rod, it would have to exert a force of 68 oz., or approximately 4.25 lbs.

You can only imagine what happens to the force when we use denser materials.

Absolute vs Relative race timing

In as much as we like to think that we're accurately timing the race, we only need a relative time to determine the order of finish. We should be able to put the triggering mechanism anywhere along the track and get the same order of finish The absolute time would be that of the time from the gate opening event to the tripping of the finish line, and would be a difficult and expensive time to gather – I doubt many units would be able to afford such accuracy. The primary thing is to have a reliable and repeatable triggering of the finish line.