User:Nydauron/Sandbox/Guides/Mousetrap Guide

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About This Guide

This guide is based on my personal experiences after doing this event. I competed in this event during the 2018 and 2019 season in Division C. While the rules aren't the same for Division B, my advice should still be applicable.

DISCLAIMER: This guide is merely to help guide you in the right direction. You are NOT going to be guaranteed first by just following this.

Objectives

Due to replaying rules for the 2021 season, the rules for Mousetrap Vehicle will most likely be very similar to the 2020 rules: get as close to a single point between 9.0m to 12.0m using a single mousetrap as propulsion.

With low score winning and score being calculated as [math]\displaystyle{ 2*(cmFromTarget) + (timeInSeconds) }[/math], there should be a higher priority to get as close as possible to the target. By going faster, your car may produce inconsistent results, while slower cars will have more predictable results. However, there needs to be a balance between speed and accuracy: too slow, and more points are gained from time, too fast and more points are gained from the offset from the target. This is where testing and revisions come into play.

The Physics Behind the Mousetrap Car

With this vehicle event having only a single mousetrap as a source of energy, the car will have a limited amount of Joules. This energy mustn't be gone wasted. If given the option of using two mousetraps (Div B is only allowed one), you should almost always use two since it provides double the potential energy. The total energy equation for our scenario is as follows:

[math]\displaystyle{ PE = KE_T + KE_R + Q }[/math] (1.1)

Where [math]\displaystyle{ PE }[/math] represents the potential energy stored into the mousetrap initally, [math]\displaystyle{ KE_T }[/math] is the translational kinetic energy, [math]\displaystyle{ KE_R }[/math] is the rotational kinetic energy, and [math]\displaystyle{ Q }[/math] is energy lost to entropy or friction. If we break down the kinetic energy labels into more abstract variables, we'll get:

[math]\displaystyle{ PE = \tfrac{Mv^2}{2} + \tfrac{I\omega^2}{2} + Q }[/math] (1.2)

Where [math]\displaystyle{ M }[/math] is mass of the object moving in kg, [math]\displaystyle{ v }[/math] is velocity of the object in m/s2, [math]\displaystyle{ I }[/math] is moment of inertia of the wheels in kg*m2, and [math]\displaystyle{ \omega }[/math] is angular velocity of the wheels in radians/s (usually expressed as 1/s since radians is a ratio).

We will go through each variable and discuss what each variable affects and how to optimize it to effectively the limited energy.

Velocity

This is pretty self-explanatory; you will want to optimize the energy equation to maximize this property if you can. The reason being is that it will greatly help in decreasing your time.

Mass

Since the only energy you start with is from the mousetrap, you have to use that energy wisely. Based on the energy equation we evaluated earlier, as you increase mass, the maximum velocity of the vehicle will decrease. For this reason, it is important to keep your car as light as possible. One way this can be done is to make the car out of balsa wood. Balsa is a very low-density wood that also has great structural integrity.

Angular velocity

Angular kinetic energy is something people might not consider normally, but in a build like this, it can dramatically affect performance. Angular velocity is referring to how fast the wheels are spinning. This factor is directly relational to translational velocity:

[math]\displaystyle{ \omega = \tfrac{v}{r} }[/math] (2.1)

Where [math]\displaystyle{ \omega }[/math] is angular velocity, [math]\displaystyle{ v }[/math] is translational velocity, and [math]\displaystyle{ r }[/math] is the radius of the wheels.

The reason how angular kinetic energy affects how your vehicle performs will become more apparent once we explain moment of inertia.

Moment of Inertia

The moment of inertia in the wheels. Moment of inertia is the property of resisting change to rotational forces. An object with a higher moment of inertia is more resistant to change in motion than an object with low inertia. Now, in a general formula, the moment of inertia of an object is calculated using integrals, something much more complex for this event. Specifically, we are going to be calculating for the moment of inertia of a cylinder (i.e., a wheel) that rotates around the centerline:

[math]\displaystyle{ I = \tfrac{mr^2}{2} }[/math] (3.1)

Where [math]\displaystyle{ I }[/math] is the moment of inertia, [math]\displaystyle{ m }[/math] is the mass of the cylinder, and [math]\displaystyle{ r }[/math] is the radius of the cylinder.

Now that we understand the components of angular kinetic energy, we can substitute these new values into the energy equation:

[math]\displaystyle{ PE = \tfrac{Mv^2}{2} + \tfrac{mr^2}{2}*\tfrac{(\tfrac{v}{r})^2}{2} + Q }[/math] (3.2)

[math]\displaystyle{ PE = \tfrac{Mv^2}{2} + \tfrac{mr^2}{2}*\tfrac{v^2}{2r^2} + Q }[/math] (3.3)

[math]\displaystyle{ PE = \tfrac{Mv^2}{2} + \tfrac{mv^2}{4} + Q }[/math] (3.4)

[math]\displaystyle{ PE = v^2(\tfrac{M}{2} + \tfrac{m}{4}) + Q }[/math] (3.5)

As can be seen, angular kinetic energy makes the coefficient of [math]\displaystyle{ v^2 }[/math] bigger (since [math]\displaystyle{ \tfrac{m}{4} }[/math] is positive), resulting in the value of [math]\displaystyle{ v }[/math] to go decrease. So, in order to maximize velocity, we will want to reduce the mass of the wheels as much as possible. We also can observe that the radius of the wheels will not affect the velocity of the car. However, while this will not affect the final velocity of the car, it will affect the acceleration of the car. Acceleration here can be seen through the use of torque:

[math]\displaystyle{ \tau = I\alpha }[/math] (3.6)

[math]\displaystyle{ \tau = \tfrac{mr^2}{2}*\alpha }[/math] (3.7)

Where [math]\displaystyle{ \tau }[/math] is the torque on the axle and wheels, [math]\displaystyle{ I }[/math] is the moment of inertia, and [math]\displaystyle{ \alpha }[/math] is the angular acceleration of the wheels. When a mousetrap vehicle that is ready-to-run is launched, the string that is wrapped around the axle tenses up and provides a consistent torque on the axle and wheels. Therefore, if we have heavy or big radius wheels, the car will start off with a slower acceleration.

In some scenarios where the car needs only to travel a short distance (<7m), acceleration becomes more critical. However, if the vehicle needs to travel a much larger distance (>=7m), you would want to optimize it to go for distance rather than speed.

Friction

A loss of energy. In almost every scenario, friction will exist. There really isn't a consistent way to measure friction, but it comes in the subtleties in design in your build. However, there are ways to mitigate the effects of friction. If you build your car without parts that help reduce friction, the vehicle will not be efficient and may not even make the target point.

One major factor that can contribute to friction is the axle rubbing against the frame of the vehicle as it rotates. This rubbing can cause the car to lose a lot of potential energy to heat if not accounted for. If you build your frame using balsa, you might even notice the axle digging into the wood. This is a clear indication that you are losing energy to friction. A straightforward way that you can use to reduce this is by putting graphite where the axle touches the frame. This should improve your car, and it should go farther, but don't expect flying colors.

In my experience, I used ball bearings. Ball bearings offer a way of holding an axle while also allowing it to rotate freely. In my build, I used tape to give the axle a snug fit when inserting it into the bearing. Once installed, and giving it a spin, you immediately notice the benefits of using bearings vs. graphite.

Some people have also submerged their bearings in WD-40 to remove the lubrication inside the bear. This will actually make your bearings even more efficient. However, the bearing will have a much higher chance of breaking up and a shorter life-span. I, personally, did not opt for this route and played it safe.

There is another type of friction that is important but will be covered in a later portion of this guide.

Design

Now that we have talked about the fundamental physics behind a mousetrap car, we now have some idea how to design the vehicle. As mentioned before, we want to have a light body frame with light wheels. However, in order to make a successful car, there are other factors to consider.

Mousetrap Placement and Arm length

The distance between your drive axle (the axle being pulled by the string) and the mousetraps determines the car's arm length. Arm length is related to two properties: acceleration and distance. Both of these properties are inversely related. As stated before, how you design your car will depend on the scenario. If the vehicle only needs to travel short distances, acceleration would be more useful. For farther targets, optimizing for distance will be more beneficial.

The reason why your arm length should be the distance between the drive axle and the center of the mousetraps is because of forces and torque. We can analyze this by using some basic physics. Say the mousetraps are in the ready-to-run position, exerting a torque on the arm. We can then say:

[math]\displaystyle{ \tau_{mousetrap} = F_{arm} l_{arm} }[/math] (4.1)

The equation we use to show the torque on the axle from the arm is:

[math]\displaystyle{ \tau_{axle} = F_{arm} r_{axle} \sin \theta }[/math] (4.2)

In the first equation, we can see as [math]\displaystyle{ l_{arm} }[/math] (the length of the arm) increases, it reduces the force provided by the arm. This causes a weaker torque on the axle and wheels, causing it to accelerate slower. A key factor in the second equation is [math]\displaystyle{ \theta }[/math]. [math]\displaystyle{ \theta }[/math] here is the angle between the arm and the string. In the ready-to-run position, if this angle is not 90 degrees, it will provide a weaker force since the tension force is a component of the force from the torque of the arm.

How Arm Length Affects Drive Distance

To determine the distance that the car will be powered by the mousetrap, we can use this simple formula:

[math]\displaystyle{ d = 2 * l_{arm} \tfrac{ r_{wheel} }{ r_{axle} } }[/math] (5.1)

Since for Div B, the objective is to only travel forward, it is not as essential to have [math]\displaystyle{ d }[/math], the drive distance, equal 9-12 meters since the car will be accelerating for [math]\displaystyle{ d }[/math] meters. For the rest of the way, the drive string can be detached, and the car can then cruise until the point where it needs to brake. However, in Div C, the vehicle needs to be able to travel forward and then backward. This means that the car must be pulled backward by the mousetrap once it has traveled the distance forward. In this case, [math]\displaystyle{ d }[/math] needs to be greater than the distance traveled forward in order to accelerate the car back. After the car has gained enough velocity, the car doesn't need to be powered by the mousetrap and can cruise to the target point.

Brakes

There are several designs for brakes that will work with your design. Most designs for brakes can be seen from other vehicle events like Wheeled Vehicle, Gravity Vehicle, and Scrambler.

String Brakes

An example of string brakes on a scrambler vehicle.

While not as common, string brakes offer a simple way of getting your car to break. This method involves tying a string to both axles which will progressively wind around one axle and unravels on the other. The brakes will cause the car to converge to a point, oscillating back and forth.

This method of braking is not the most efficient design, nor is it the most accurate, but it will get the job done.

Wingnut Brakes

Wingnut brakes are more widely known can be seen on a variety of builds. This method uses a wingnut that traverses across the threaded axle. With the help of a rod or dowel, the wingnut stops spinning and starts to move along the threads. The wingnut will continue to move until it hits a locknut, locking up the wheels. This sudden lock up will cause the vehicle to stop in its tracks.

An example of wingnut brakes on a scrambler vehicle.

Wingnut brakes are one of the more preferred brake designs simply because of its efficient braking. It also can be very accurate since the string in string brakes can thin and become inconsistent. The only downside is that the car (especially if the car is heavy or the wheels have a high moment of inertia) is skidding. In a competition where you want to get as close as possible to a Target Point, you want to try to avoid or at least minimize inconsistent factors in your builds.

Which Axle for What

While you might use both axles for string brakes, but one axle should be used for driving and then one for braking. Especially when braking, the different axles will produce different results. If you have front axle brakes, your car will almost lean into the brakes and absorbs most of the kinetic energy quickly. However, with rear axle braking, the car doesn't lean into the brakes and instead causes the brakes to lag behind. This can cause the brakes to skid as the car continues to move forward. When it comes to precision and repeatability, it is more desirable to reduce skid between the ground and the wheels. Therefore, I would recommend using front-axle brakes.

If the objective needs the car to go backwards to the target point, it is best to put the brakes in the rear. This way, on the reverse, the car's brakes will be optimal and will reduce possible skidding. The front axle can then be set up to drive the vehicle. However, if your car only needs to go forward, it is best to keep the brakes in the front and keeping the drive axle in the rear.

Static Wheel Friction

While you do not want kinetic friction when transferring the potential mousetrap energy to translational kinetic energy, you want to have high static friction on your wheels against the ground so that they do not lose traction. I many cases, if you accelerate too fast, the wheels will not be able to grip the floor and will thus skid. This is horrible since it wastes the precious limited mousetrap energy. If the vehicle is experiencing these issues, there might be ways to increase static friction depending on what wheels you are using.

If you are using CD wheels (120mm or 80mm), I would recommend you try to use balloons. The rubber can be wrapped around the edges of the CD providing a solid grip to surfaces. If you want to step it up, I would say to go for heavy duty rubber gloves. These are usually thicker and grippier gloves than the balloons and can help you achieve higher speeds.

Other options would be to go for a different wheel. Wheels like BaneBots T40 wheels provide a spongey and sticky surface to grip the floor. These wheels are a great choice if you are planning to build the car from scratch rather than modifying an old vehicle which might have different compatibilities.