Lightning+Racer12

=__**Lightning Racer**__= By Austin Tarman, Nate Pardoe, and Joshua Pardoe.



The Lightning Racer became the first wooden racing/dueling coaster in the United States when it was built in 2000 by Great Coaster International. It is a double-track wooden roller coaster constructed with Southern Yellow Pine wood with two staggered lifts. Each Train of cars can hold up to 24 people so even though it is a popular ride, the line is not as long as one would expect. In the polls, it consistantly ranks in the top 10 in the golden Ticket awards and top 25-35 in the Mitch Hawker's best roller coaster poll for their wooden division. In order to explain the physics of the Lightning racer, some measurements were gathered and other data recorded. To start, with a stopwatch, the total time from when the ride started to move to when it crossed the finish line was taken. A GLX inside a special vest was worn while ridding the ride to record the acceleration in three directions. The angle above the horizontal at two spots (from eyesight) with the distance in paces between was taken to the top of the first big hill and for the finish line. Next, the time for the entire length of the train of cars to pass a point was taken with a stop watch at the top of the first big hill, bottom of that hill and at the finish line. For each set of data, 3 good trials were taken so that they could be averaged together to become more accurate. The length of the train of car on the ride was measured in paces. The height of the first hill, mass of the train of cars, and length of the tracks were found online.

__Total Time__ __Basic Measurements__ 10.25ft = 5 steps Length of Train = 18.25steps Mass of Train= 5171kg Length of Track = 3393ft __Height of Hill one__ 91.6ft __Top of Hill 1__ __At Finish Line__ Angles to top 6.5 and 11 degrees with 36 steps separating them __Bottom of Hill 1__ The height is approximately .50 meters above the ground.(Height is Taken from the middle of the trains height at all locations) **Calculations**
 * Data**
 * Thunder (s) || Lighting (s) ||
 * 153.95 || 153.95 ||
 * 153.58 || 152.97 ||
 * 152.72 || 152.67 ||
 * Thunder's Time to Cross (s) || Lighting's Time to Cross (s) ||
 * 4.74 || 4.21 ||
 * 4.31 || 4.81 ||
 * 5.21 || 4.75 ||
 * Thunder's Time to Cross (s) || Lighting's Time to Cross (s) ||
 * 1.99 || 1.26 ||
 * 1.78 || 1.30 ||
 * 1.44 || 1.43 ||
 * Thunder's Time to Cross (s) || Lighting's Time to Cross (s) ||
 * 0.53 || 0.57 ||
 * 0.79 || 0.6Area = 136.4m/s = Total Velocity ||
 * Calculations**

The distance of 5 paces was measured at home so that the distance per pace could be calculated by taking the distance in inches and converting it into meters and then dividing by 5. Thus, with that, the length of the train of cars could be found and then divided by the average time for the train to pass any point to find the instant speed at that point. The total average speed for the path of the ride was calculated by dividing the length of the ride to the finish line by the time it took to complete that distance. The angles and distance between them mentioned above can be plugged into a formula given online to find the height at a specific location on the track. With the velocity, height, and mass at each point, the potential and kinetic energy can be calculated for each point. The kinetic energy formula is (1/2)mv^2 and the formula for potential gravitational energy is mgy. The conservation of energy is the main concept behind this ride because it is carried up very high so it can gain a lot of potential energy and it uses that energy to power the rest of the ride.

__Length of One Step__ 10.25ft =5 step 10.25(12)=123in 123(2.54)= 312.4cm 312.4/100= 3.124m 3.124m= 5steps //1 step = 3.124/5 =.625m// __Length of Trains__ 1 Train = 18.25step 1 step = .625m 1 Train = 18.25(.625) = //11.40m//

**Average Velocity** V=x/t __Thunder__ x =3393ft(3.38)=1034m t= 153.42 v= 1034/153.42 = //6.74m/s// __Lighting__ x = 1034 t= 153.20 v= 1034/153.20 = //6.75m/s//
 * || Thunder Total Time (s) || Lighting Total Time (s) ||
 * || 153.95 || 153.95 ||
 * || 153.58 || 152.97 ||
 * || 152.72 || 152.67 ||
 * Average || 153.42 || 153.20 ||

__**Top of the Hill**__ V=x/t __Thunder__ x=11.40 t=4.75 v=11.40/4.75=//2.40m/s// __Lighting__ x=11.40 t=4.59 v=11.40/4.59 =//2.48m/s// E = mgy +1/2mv2 m= 5171 g=9.8 y =91.6ft/3.28=27.92m mgy= 5171(9.8)27.92 = 1.41E6J __Thunder__ m=5171 v= 2.40 .5mv2= .5(5171)(2.40)2= 14890J total = 14890+1.41E6= //1.43E6J// Lighting m=5171 v= 2.48 .5mv2= .5(5171)(2.48)2=15900J total =15900+1.41E6= //1.44E6// V=x/t __Thunder__ x=11.40 t= .66 v=11.40/.66 = //17.3m/s// __Lightning__ x=11.40 t =.63 v=11.40/.63=//18.1m/s// E = mgy +1/2mv2 m= 5171 g=9.8 y =.50m mgy= 5171(9.8)=24713J __Thunder__ m=5171 v= 17.3 .5mv2= .5(5171)(17.3)2= //7.74E5J// total = 7.74E5+24713= 7.99E5J Lighting m=5171 v= 18.1 .5mv2= .5(5171)(18.1)2=//8.47E5J// total =8.47E5+24713= 8.72E5EJ
 * Velocity**
 * || Thunder's Time to Cross (s) || Lighting's Time to Cross (s) ||
 * || 4.74 || 4.21 ||
 * || 4.31 || 4.81 ||
 * || 5.21 || 4.75 ||
 * Average || 4.75 || 4.59 ||
 * Energy **
 * __At Bottom of First Hill__**
 * Velocity **
 * || Thunder's Time to Cross (s) || Lighting's Time to Cross (s) ||
 * || 0.53 || 0.57 ||
 * || 0.79 || 0.69 ||
 * Average || 0.66 || 0.63 ||
 * Energy **

__**At Finish**__ __Velocity__ v=x/t __Thunder__ x=11.40 t=1.74 v=11.40/1.74=6.55m/s __Lightning__ x=11.40 t=1.33 v=11.40/1.338=8.57m/s
 * || Thunder's Time to Cross (s) || Lighting's Time to Cross (s) ||
 * || 1.99 || 1.26 ||
 * || 1.78 || 1.30 ||
 * || 1.44 || 1.43 ||
 * Average || 1.74 || 1.33 ||
 * Height**

(sin ϕ1(sinϕ2))/sin(ϕ2-ϕ1)L=h L=.625(36)=2249m  (sin6.5)*sin(11)/(sin11-6.5)22.49= (.0216/.07845)22.49=.275(22.49)=6.19 6.19 +1.65 (Nate's height to eye)= 7.84m E = mgy +1/2mv2 <span style="font-family: Times New Roman,serif;">m= 5171 g=9.8 y =7.84m mgy= 5171(9.8)7.84 = 3.97E5J __Thunder__ <span style="font-family: Times New Roman,serif;">m=5171 v= 6.55m/s .5mv2= .5(5171)(6.55)2= 1.11E5J total = 1.11E5+3.97E5= //5.08E5J// Lighting <span style="font-family: Times New Roman,serif;">m=5171 v= 8.57 .5mv2= .5(5171)(8.57)2=1.90E5J
 * <span style="font-family: Times New Roman,serif;">Energy **

**<span style="font-family: Times New Roman,serif;">total =1.90E5+3.97E5= //5.87E5J// **
The GLX was used to find the the horizontal acceleration (x), vertical acceleration (y), and sideways acceleration (z). The graphs can show different parts of the ride like when it just took off, climbed up the first big hill, when it went down that hill, and at the finish line. The area under each GLX graph represents each the average velocity in their respective directions. Total Velocity = Area = __136.4m/s__
 * __Acceleration Graphs of Thunder__**
 * X Acceleration**

Total Velocity = Area = __1004.0m/s__
 * Y Acceleration**

Total Velocity = Area = __549.8m/s__
 * Z Acceleration**

__**Points**__
 * 1) The little drop to increase velocity before the starting hill
 * 2) The time as the train is being towed up the starting hill
 * 3) At the top of starting hill going down
 * 4) Going down the second hill
 * 5) Curving around the turnaround at the far side

http://coasterkev.homestead.com/Favorites.html http://www.hersheypark.com/rides/details.php?id=2 http://rcdb.com/597.htm http://coasterbuzz.com/RollerCoasters/lightning-racer
 * Sources**