Re: Gravity Vehicle C
Posted: October 5th, 2011, 5:16 am
OK, time to wind into a little string theory…..maybe we can do quantum entanglement next week.
I think the variability being discussed is much more attributable to how the string wound and unwound, and what kind and size of string, than the finish of the floor. This understanding comes from both a couple years of MTVs, and before that, Electric vehicles. The other factor to remember in applying experience from MTVs to GVs is the differences in mass of vehicle, and the energy available. Because of the limited power of a mousetrap, and the score value of speed, you needed to get the mass of an MTV down as far as possible. With a weight of up to 2.5kg, and almost a meter of “g” to accelerate it, a GV is a very different critter; MUCH more momentum at MTV velocities; much, much more at the sort of velocities we’ll be seeing – especially at shorter distances-5, 6, 7m.
Let’s think about what the variables are:
First, is the extent to which a string stretches. Obviously, you don’t want any stretch. Think Kevlar. There are at least a couple of brands of fishing line (Spider Wire being one) made of Kevlar. It stretches the least of the commonly available…..string-like materials I’m aware of. It comes in a wide range of sizes- from a few thousandths of an inch diameter with a tensile strength of a few kg, to larger diameters and strength of 50+ pounds.
Next is how it winds onto an axle. Unless you have built in a feeding control system, its going to vary from run to run; the extent to which it spreads out along the axle, or “balls up” on a limited length of axle. That can have a big effect. How big depends on a couple of inter-related factors. 1) the diameter of the axle its winding onto vs the diameter of the wheel, and 2) the diameter of the string vs the diameter of the axle.
Then, let’s look at an example.
Wheel diameter (Dw) of 10cm (100mm)= wheel circumference (Cw) of 314mm. Axle diameter (Da) of 3mm = axle circumference of 9.42mm. So, for each meter (100 cm, 1000mm) traveled, if the string winds onto the axle in a single layer, you’ll pull roughly 29.9mm of string. So what happens as the string starts to “layer” on the axle?- 3, 4, 5 layers of string? Let’s look at two string possibilities, one at 0.05mm, one at 0.1. Let’s look at these diameters at 3 layers of string, and at 6 layers. Small string first; at 3 layers, Da = 3mm+0.15mm=3.15mm; Ca=9.9mm. Traveling one meter (3.18 revolutions of your wheel) at that effective axle winding diameter, you pull 31.5mm of string; at 6 layers, Da=3.0mm+0.3mm=3.3mm=Ca of 10.36, or 32.95mm of string for 1m traveled. So, the difference in string length, for 1m of travel, from 3 layers of winding, to 6 layers is from 31.5mm to 32.9mm; 1.4mm. That’s roughly 14% of the circumference of the axle (using the average of the two Da-s), but 14% of a revolution of a wheel (Cw)is about 44mm-4.4cm, so at a distance of 5m, you have about a 22cm variation in distance; at 10m that variation is up to 44cm.
With bigger string, the effect magnifies. Big string now; at 3 layers, Da = 3mm+0.3mm=3.3mm; Ca=10.36mm. Traveling one meter (3.18 revolutions of your wheel) at that effective axle winding diameter, you pull 32.95mm of string; at 6 layers, Da=3.0mm+0.6mm=3.6mm=Ca of 11.3, or 35.95mm of string for 1m traveled. So, the difference in string length, for 1m of travel, from a single layer of winding, to 6 layers is from 32.95mm to 35.95mm; 3mm. That’s about 28% of the circumference of the axle, and 28% of a revolution of a wheel is about 88mm-8.8cm, so at a distance of 5m, you have about a 44cm variation in distance; at 10m that variation is up to 88cm.
So, what does this tell us?
First, the variability in winding patterns introduces a fundamental problem w/ a system of a string wound around both axles- where it unwinds from onto the other. If at any point, the feed rate from the unwinding axle is less than the wind rate of the winding axle, you get binding, i.e., braking. If the unwinding rate is faster than the winding rate, you get loose string, and all kinds of bad (and unpredictable) things can happen. You want to use string that doesn’t stretch. You want it to wind the same way each time (all kinds of fun engineering possibilities to make that happen). You want to use the smallest string that’s strong enough. Remember, though, 2.5kg moving at, oh, a couple meters/sec is a lot more energy than you may be used to with a MTV. Two variables to play with here- bigger string, or a bigger axle winding diameter (think leverage- you could put a collar, or a winding wheel on the axle- significantly bigger than the axle diameter; more string to manage, but the pull on the string to stop the vehicle will be less.
Last, when you look at how the scoring system works, you should realize how important reliable, consistent braking is (along with getting a vehicle that rolls straight); the points value of 1 second difference in run time (50 points) is the same as 5cm in accuracy. At 5m, there is not going to be a lot of time difference between…..reasonably well engineered vehicles; maybe ½ a second; 25 points. 25mm (2.5cm) difference in how close to the target you get a) gets you the same points, and b)is a pretty small distance. Controlling precision is going to be the key to a good score.
Fun stuff to think about, huh?
I think the variability being discussed is much more attributable to how the string wound and unwound, and what kind and size of string, than the finish of the floor. This understanding comes from both a couple years of MTVs, and before that, Electric vehicles. The other factor to remember in applying experience from MTVs to GVs is the differences in mass of vehicle, and the energy available. Because of the limited power of a mousetrap, and the score value of speed, you needed to get the mass of an MTV down as far as possible. With a weight of up to 2.5kg, and almost a meter of “g” to accelerate it, a GV is a very different critter; MUCH more momentum at MTV velocities; much, much more at the sort of velocities we’ll be seeing – especially at shorter distances-5, 6, 7m.
Let’s think about what the variables are:
First, is the extent to which a string stretches. Obviously, you don’t want any stretch. Think Kevlar. There are at least a couple of brands of fishing line (Spider Wire being one) made of Kevlar. It stretches the least of the commonly available…..string-like materials I’m aware of. It comes in a wide range of sizes- from a few thousandths of an inch diameter with a tensile strength of a few kg, to larger diameters and strength of 50+ pounds.
Next is how it winds onto an axle. Unless you have built in a feeding control system, its going to vary from run to run; the extent to which it spreads out along the axle, or “balls up” on a limited length of axle. That can have a big effect. How big depends on a couple of inter-related factors. 1) the diameter of the axle its winding onto vs the diameter of the wheel, and 2) the diameter of the string vs the diameter of the axle.
Then, let’s look at an example.
Wheel diameter (Dw) of 10cm (100mm)= wheel circumference (Cw) of 314mm. Axle diameter (Da) of 3mm = axle circumference of 9.42mm. So, for each meter (100 cm, 1000mm) traveled, if the string winds onto the axle in a single layer, you’ll pull roughly 29.9mm of string. So what happens as the string starts to “layer” on the axle?- 3, 4, 5 layers of string? Let’s look at two string possibilities, one at 0.05mm, one at 0.1. Let’s look at these diameters at 3 layers of string, and at 6 layers. Small string first; at 3 layers, Da = 3mm+0.15mm=3.15mm; Ca=9.9mm. Traveling one meter (3.18 revolutions of your wheel) at that effective axle winding diameter, you pull 31.5mm of string; at 6 layers, Da=3.0mm+0.3mm=3.3mm=Ca of 10.36, or 32.95mm of string for 1m traveled. So, the difference in string length, for 1m of travel, from 3 layers of winding, to 6 layers is from 31.5mm to 32.9mm; 1.4mm. That’s roughly 14% of the circumference of the axle (using the average of the two Da-s), but 14% of a revolution of a wheel (Cw)is about 44mm-4.4cm, so at a distance of 5m, you have about a 22cm variation in distance; at 10m that variation is up to 44cm.
With bigger string, the effect magnifies. Big string now; at 3 layers, Da = 3mm+0.3mm=3.3mm; Ca=10.36mm. Traveling one meter (3.18 revolutions of your wheel) at that effective axle winding diameter, you pull 32.95mm of string; at 6 layers, Da=3.0mm+0.6mm=3.6mm=Ca of 11.3, or 35.95mm of string for 1m traveled. So, the difference in string length, for 1m of travel, from a single layer of winding, to 6 layers is from 32.95mm to 35.95mm; 3mm. That’s about 28% of the circumference of the axle, and 28% of a revolution of a wheel is about 88mm-8.8cm, so at a distance of 5m, you have about a 44cm variation in distance; at 10m that variation is up to 88cm.
So, what does this tell us?
First, the variability in winding patterns introduces a fundamental problem w/ a system of a string wound around both axles- where it unwinds from onto the other. If at any point, the feed rate from the unwinding axle is less than the wind rate of the winding axle, you get binding, i.e., braking. If the unwinding rate is faster than the winding rate, you get loose string, and all kinds of bad (and unpredictable) things can happen. You want to use string that doesn’t stretch. You want it to wind the same way each time (all kinds of fun engineering possibilities to make that happen). You want to use the smallest string that’s strong enough. Remember, though, 2.5kg moving at, oh, a couple meters/sec is a lot more energy than you may be used to with a MTV. Two variables to play with here- bigger string, or a bigger axle winding diameter (think leverage- you could put a collar, or a winding wheel on the axle- significantly bigger than the axle diameter; more string to manage, but the pull on the string to stop the vehicle will be less.
Last, when you look at how the scoring system works, you should realize how important reliable, consistent braking is (along with getting a vehicle that rolls straight); the points value of 1 second difference in run time (50 points) is the same as 5cm in accuracy. At 5m, there is not going to be a lot of time difference between…..reasonably well engineered vehicles; maybe ½ a second; 25 points. 25mm (2.5cm) difference in how close to the target you get a) gets you the same points, and b)is a pretty small distance. Controlling precision is going to be the key to a good score.
Fun stuff to think about, huh?