USEFUL APPS
MEASURING TIMES
![Picture](/uploads/1/4/0/9/14098772/275512453.jpg?149)
Several of the lab activities require you to measure a time, for example, the time it takes the roller coaster to travel from the top of the hill to the bottom. Most of the time, this is best done while you are not on the ride. Instead, if you have a good vantage point to view the ride from, measure the time while you are on the ground. This can be done best while you are waiting in line for a ride, or along the exit to the ride after you get off. There are a few circumstances, where you will not be able to view the part of the ride you must time unless you are physically on the ride. In that case, you will have to take the time while you are riding. Use a stopwatch or the stopwatch function on a digital watch (most smart phones come with a stopwatch function). It is best to measure the time several times and average those values.
MEASURING DISTANCES
There are several good ways to determine a distance measurement. The best way, may depend on what distance you are measuring.
![Picture](/uploads/1/4/0/9/14098772/492809394.jpg?185)
String measurement (the best method) – This is the method Homer Hickam used in the movie “October Sky” to find his lost rocket. It is useful for measuring long distances and can be more accurate than pacing. Carrying a tape measure around an amusement is not easy, but your group may want to carry a set length of string. How long a string and what type of string to use is up to your group, but 5-10 m is probably best. You want to choose a string thin enough that when it is rolled up in a ball or around an index card it easily tucks into your pocket or purse, but thick enough that it does not tangle easily. It would also be a good idea to mark off every half meter to meter on your string.
![Picture](/uploads/1/4/0/9/14098772/4796016_orig.jpg)
Uniformity in Structure (AVOID if possible) - Another way to estimate distances is to use uniformity in the structure to guide your estimate. It is difficult to accurately estimate large distances; however, small distances (like 1 – 2 meters) can be easily and reasonably estimated. If a structure has a repeating small pattern then you can estimate the length of the small pattern and count how many times the pattern repeats itself throughout the structure.
![Picture](/uploads/1/4/0/9/14098772/118995211.jpg?149)
Pacing (AVOID at all costs)– Pacing is a good way to measure long straight distances. You should determine your pace length before you go to the amusement park. You can then pace off lengths at the amusement park and determine the total length. For example, if you need to know the length of a train of cars on a roller coaster, you can pace the length of the train on the deck just before you get on or after you get off the ride. Pacing inherently has errors. To help reduce these random errors it is a good idea for each member of your group to pace the length separately and then average the distances.
MEASURING HEIGHTS
Using Similar Triangles and Shadows – This method is simple, fast, and relatively accurate, but requires that you can measure the length of the shadow of the object whose height is in question. If the sun is not shining, or you cannot get to the base of the object, another method will be required.
- Measure your height, h0
- Measure the height of your shadow, S0
- Measure the height of the shadow of the object, S1
- Use the ratios h0/S0 = h1/S1, and some algebra to get h1 = h0S1/S0
Using Similar Triangles and Reflections – This method is also simple, fast, and relatively accurate, and does not require shadows from the sun. It does however require the use of something reflective, such as a mirror (be careful to avoid breakage!), and you will need to be able to get to the base of the object.
- Place the mirror on the ground (and have a lab partner warn passers-by not to step on it!)
- Stand so that you can just see the top of the object in the mirror.
- Measure your eye height, he
- Measure your distance from the mirror D0
- Measure the height of the shadow of the object, D1
- Use the ratios he/D0 = h1/D1, and some algebra to get h1 = heD1/D0
Triangulation – You can use the horizontal accelerometer as a sextant (an angle measuring device) to aid in measuring the heights of objects that are too tall to measure directly, such as the height of a tall building. You can measure heights with reasonable accuracy with a little trigonometry. The process is outlined below.
1. Measure the distance S by using your string or some other method. Because of security fences, sometimes is will be difficult to get right up against the ride you are trying to measure the height of. You will need to get as close as possible and then estimate the remaining distance or choose to double triangulate (see below).
2. Sight through the straw on the top of the horizontal accelerometer (sextant) to the top of the object you are trying to determine the height of. Measure the angle on the sextant from the middle BB.
3. Measure h0, which represents your height to your eye level.
4. Calculate h1 using the following equation. h1 = S tan (THETA).
5. The total height you are trying to measure, H, is equal to h0 + h1.
1. Measure the distance S by using your string or some other method. Because of security fences, sometimes is will be difficult to get right up against the ride you are trying to measure the height of. You will need to get as close as possible and then estimate the remaining distance or choose to double triangulate (see below).
2. Sight through the straw on the top of the horizontal accelerometer (sextant) to the top of the object you are trying to determine the height of. Measure the angle on the sextant from the middle BB.
3. Measure h0, which represents your height to your eye level.
4. Calculate h1 using the following equation. h1 = S tan (THETA).
5. The total height you are trying to measure, H, is equal to h0 + h1.
Double Triangulation – Most of the time you will not be to stand right up against the object whose height you are trying to measure. This will make measuring the distance S very difficult. If you cannot reasonably estimate the distance from the fence to the base of the ride, then you may want to use double triangulation. The method is outlined below.
- Stand as close as you can to the object and measure the angle theta 2 with your sextant from the middle BB.
- Use your string to measure some distance, D, away from the ride (the longer the distance the better).
- Measure the shallower angle theta1 with your sextant again from the middle BB.
- With a little trigonometry, it can be shown that the distance h1 can be found from the following equation. h1 = (D) (sinq1 )(sinq2) / sin(theta2 - theta1)
- Measure h0, which represents your height to your eye level.
- The total height you are trying to measure, H, is equal to h0 + h1.
MEASURING ACCELERATION
![]() ACCELEROMETERS: We have some accelerometer probes that we can send with you on the rides, just be sure not to drop them, or better yet, put the WDSS in a vest and look stylish! (Don’t forget to press record…)
If sensors aren’t available, one can still use a mass on a spring to build a vertical accelerometer, and you may see these in use. Use the vertical accelerometer to measure the g-forces experienced on different rides. Accelerometers measure accelerations by measuring forces. The accelerometer is calibrated in units of “g”. The constant “g” is related to the acceleration due to gravity. When a person is standing still on the surface of the earth the accelerometer should read 1 g. This means that you are experiencing the force of gravity. A reading of 2 g on an accelerometer does not mean that the gravitational field has increased. It means that the rider feels a force, which is twice the magnitude of the rider’s weight, 3 g’s equals three times a person’s weight and so on. The accelerometer reads how many g-forces you are experiencing at any one time. Remember that on a ride you are experiencing both the force of gravity + or - the ride forces. When you and the accelerometer are upside-down, the force of gravity is pulling the bob toward the top of the accelerometer, not down. When the bob rises to the 0 g mark then you are in free fall. OTHER WAYS TO OBTAIN DATA![]() Some physical data about particular rides can be obtained from other sources as well. One place to check for information about each ride is on the amusement parks website. Some of the rides do list specific information, like heights, weights, etc. Be sure the information listed is in fact what you are looking for to complete the lab. Sometimes you may not need the maximum height of a ride, but the height that the roller coaster car actually reaches. Another place you may be able to obtain information about a ride is from the people that work at the park. Let me caution you about this information. Sometimes, a ride technician may know what he/she is talking about, other times, they may flat out be lying to you or giving you false information to sound knowledgeable or to make the ride seem more spectacular than it actually is. Finally, never completely rely on these alternative forms of obtaining measurements. Use them as a backup to check your own measurements on only rely on them when they verify that your measurements are way off. Remember, it always helps to get as much data as possible to get the most accurate results and always state where you got the data from.
PRACTICE COLLECTING DATA![]() Look for these signs next to rides at the park - most likely the data can be collected while in line! To practice, scan the QR code to the right, or just click here
|