Finding Proper Gears and Wheels pt.ii

Finding Proper Gears and Wheels pt.ii

Gears are what make your Junior Solar Sprints car move. Finding the proper gear ratio for your car is an extremely important component of your car. Without it, your car will either struggle to get off the line, or struggle to move quickly enough to win a race. In this document we will discuss a how to find the most effective gear ratio for your car. Speed vs. Torque The following equation which the relationship between speed and torque: Power = Speed Torque Torque is the amount of force required to rotate an object, while speed is how quickly something rotates. Power is the output of the motor. Since everyone is using the same motor we can safely assume that power is fairly equal between cars. If we know that the power is a set limit, lets say 10 kw (kilowatts) use the formula to solve the following equations: 10 = 2, 000 T, solve for T 10 = S 150, Solve for S What impact might your findings/answers have on your car s ability to move? What, if anything, can you determine about the relationship between Torque and Speed?

Experiment #1 For this experiment you will need a bicycle with gears on it, preferably one that has different settings for both the front gears and the rear gears. Safely, take the bicycle and flip it upside down so that it is resting on the handlebars and the seat. Now change the gears to different settings and pedal the bicycle. Do this a few different times and record your results in the table below. *Journal Photo Opportunity* Large Gear [# of teeth] Small Gear [# of teeth] Ratio & Speed or Torque [Large Gear : Small Gear] Easier or harder than previous setting? Gear Ratios and Wheel Size Now that we understand gear ratios, let s move on to figure out the best wheels to use. You may not have even thought about how the size of your wheel may impact your gear ratio or how your gear ratio effects the size of your wheels. They do. We are going to utilize a handy tool that I have created to do this for us. In order to complete this process without the tool you will have to perform a series of math problems to figure out your answers. The steps for this process following this page just in case you would like to try it for yourself! The tool is located {HERE} Thinking of some of the different gear ratios and wheel sizes that you might want to use for your car fill out the following charts with the information that is generated.

Finding Wheel Size Utilizing the excel document you will need to input both the driver gear (the one attached to your motor) and the driven gear (the one attached to your axle). After that you can input the other numbers that you found: Driver Gear 40 Driven Gear 10 Track Distance (cm) 2,000 Motor Speed (rpm) 5,200 Average Vehicle Time (s) 6.50 Vehicle Speed (cm/s) 307.69 Gear Ratio 0.25 Speed of the wheel (rpm) 20,800 Revolutions/Second 346.67 Wheel Circumference (cm) 0.89 Wheel Diameter(cm) 0.28 Wheel Diameter (in) 0.11 Finding a Gear Ratio (Known Wheel Size) Input the diameter of the wheel that you would like to use, in centimeters, and write down the other numbers that follow: Wheel Diameter (cm) 40 Wheel Circumference (cm) 125.7 Wheel Speed (rps) 2.4 Revolutions/minute 143.2 Gear Ratio 36.3

Finding Gear Ratios and Wheel Size If you would like to see how to determine your gear ratios or wheel size by hand, below is the process you will need to follow to determine them. Known Information: Motor Speed, ω: 5,200 revolutions per minute (rpm) Vehicle Speed, V: Finishing times average ~6.5 seconds Track Distance: 2,000 cm 2,000 cm V = = 308 cm/s 6.5 s The following is the process to find the wheel size from a known gear ratio. Step 1: Determine your Gear Ratio N = Number of gears N m= Gear attached to the motor N d = Gear attached to the axle R = Ratio Nd R = N d N m = 16 8 = 2 Step 2: Find the speed of the wheel Nm ω m = 5200 2 = 2600 rpm But we need the wheel speed in revolutions per second (rps) ω d = 2600 revolutions 1 min 1 min 60 s = 43.3 rps Step 3: Calculate wheel circumference C = Circumference C = V ω d = 308 cm/s 43.3 rps = 7.11 cm Step 4: Determine the wheel diameter, D w D w = C π = 7.11 = 2.26 cm 3.14 Step 5: Check calculation Now check to make sure that the diameter of your wheel is bigger than the diameter of the driven gear. If it is, you re all set! If not, you need to choose smaller gears.

Finding Gear Ratio with Known Wheel Size In this example we already know what wheels we would like to use, we just need to find a good gear ratio. Our wheel diameter for this example, D w, is 10 cm. Step 1: Calculate Circumference, C C = π D = 3.14 10 = 31.4 cm Step 2: Find the wheel speed, ω d ω d = V C = 308 cm/s 31.4 cm = 9.8 rps Now we need to convert that into rpm (Revolutions per minute) Step 3: Determine the gear ratio. ω d = 60 sec min R = ω m ω d = rev 9.8 = 588 rpm sec 5200 rpm 588 rpm = 8.8 So if you would like to utilize the wheel you have picked out you will need a gear ratio of 8.8, which would be any combination of Driven gear / Driver gear. If you were searching for a good gear ratio to use you would probably choose a 10 tooth gear on the motor and an 80 tooth gear on the axle, or you would need to pick out a smaller wheel.