Effective Gear Ratios

[Intragration]

now if you change the tires circumference to say 80" and leave the 4:1 gear and roll the tire one complete revolution, it will move 80" and turn the yoke 4 times, same amount of mechanical reduction (4 turns into 1) but the distance is different, so if you compare the 50" tire to the 80" tire 50/80x4.00=2.50 with the 80" tire you are turning the same amount of rpms to cover a different distance, so that effectively transforms the performance of the 4.00 gears into a 2.50 ratio, BUT only when you compare it to the 50" tire and that has been my hang up, what was the effective transformation of the 4.00 gear with 50" tires? there is no way to get a value for this unless you have another value for comparison, that bugs me

What you're asking, it sounds like to me, is how to compare the 50" tire with the 50" tire, and again, I'm saying, it is a 1:1 ratio. A 50" tire through 4.00 gears is precisely a 50" tire through 4.00 gears. THAT is your answer. It's kind of like throwing a dart at a spot in the wall and asking "how much higher is it?" Higher than WHAT? It just IS. It is exactly where it is, and it is only where it is. If you throw a second dart near the first one, then you can ask the question. But if there's only one dart, the question is not logically valid until you specify what you're comparing it to. Another example, if you throw marble on the ground and ask which direction the imaginary line that passes directly through the center of the marble is pointing. It's impossible to say. There are infinite lines that pass through that point. If you throw down a second marble, there is only one possible line between those two points. It is the same when you name any tire size, and only that tire size, and ask how that tire size affects your final drive ratio. It DOESN'T, unless and until you specify something to compare it to.

 

[pontiacgp]

8)

 

[ReQ]

again I should stress, this is all for fun more or less, I am only using my racecar for an example since thats what I have, I could of used my truck I suppose, my only reason for this discussion is simple information gathering, not trying to solve a problem, my racecar is easy.. I stick it in low gear and drive in a circle 23 times a night, I could remove all the other gears from the transmission and only keep low and reverse, except the rules in this class do not allow it..

It's kind of like throwing a dart at a spot in the wall and asking "how much higher is it?" Higher than WHAT? It just IS. It is exactly where it is, and it is only where it is. If you throw a second dart near the first one, then you can ask the question. But if there's only one dart, the question is not logically valid until you specify what you're comparing it to.

this example is a very good metaphor, I think using this will help me better explain what I am talking about, lets assume that the ground is your baseline point of reference, the axle with no tire on it should turn at a 1:1 and have such a small circumference lets just call it null (or having no value) and make this the baseline, if you throw the dart at the wall and it sticks 50" above the ground, can you compare that dart to the baseline of the ground and get a working number for how much further that dart is when compared to the baseline of the floor? is that even possible since the baseline still has no real value to speak of apparently

what I have been trying to figure out is fundamentally a flawed question I believe at this point, I was trying to say if you have THESE gears and run THIS tire, it will effect how the car preforms, but I wanted to remove the tire from the equation and explain that change in performance by applying a new number to the gear ratio based on that tire, however that does not seem to be possible, if you install a different size tire and do not know the measurements of the old tire, then performance of the car has changed due to the tire size changing, but the effect cannot be calculated because all it did was change the RPM to MPH ratios, and I guess there is no way to look at what RPM you are turning and what MPH you are traveling, and equate that to a gear ratio

I understand that the "effective" gear ratio calculation is simply an observation of the changes made by using a different size tire with the same gear setup, and nothing is really changing except the RPMs your engine will see relative to the MPH, and thats all there is too it really, I was just trying to find out if you can put a value on the perceived changes to a gear ratio by simply putting a tire on the axle, but I suppose there is no real way to do this

 

[bill]

Ideally there is no tire on the axle to get correct information about ratios...however, without tires, the car doesnt move very well. So we start out with a "normal" tire number to get a base, and then move on from there.....

 

[Intragration]

this example is a very good metaphor, I think using this will help me better explain what I am talking about, lets assume that the ground is your baseline point of reference, the axle with no tire on it should turn at a 1:1 and have such a small circumference lets just call it null (or having no value) and make this the baseline, if you throw the dart at the wall and it sticks 50" above the ground, can you compare that dart to the baseline of the ground and get a working number for how much further that dart is when compared to the baseline of the floor? is that even possible since the baseline still has no real value to speak of apparently

I think I see where you're going with this. You're basically talking about a "wheel" that is infinitely small, that represents the centerline of the axle, right? The problem with this is that, if the "wheel" really is infinitely small, and if you placed it in the ground, started the engine, placed it in gear and revved the engine to 5,500 RPM, or a billion RPM, you could sit there for eternity, and the car would never move, because an infinitely small wheel will take an infinite amount of time to travel any non-zero distance. So if I'm right and you're talking about an infinitely small wheel, that won't work, it's like dividing by zero, you have to pick something larger than infinitely small. And as soon as you pick something larger than infinitely small, well then you have something to compare with, but it doesn't sound like that's what you're looking for. And with your response to the dart analogy, the correct way to phrase that particular question about the one dart and the floor would be "what is the ratio between the height of the dart from the floor and the height of the floor from the floor?" :shock: If you plug these numbers into Windows Calculator, the actual answer you get back is "cannot divide by zero". You should have called this thread "brain teasers".

 

[ReQ]

You should have called this thread "brain teasers".

my brain feels more broken than teased at this point I hate the situation of being smart (relatively speaking) enough to ponder a question, but smart enough not answer it, I feel like the answer is right on the tip of my tongue, but still out of reach

I keep trying to remove different aspects of the equation to suit my needs at any given point, but I realize that is only causing the question to be impossible to answer, the engine/transmission/differential AND tires all need to be accounted for or this cannot work, I am basically trying to remove the tires from the equation, get a "baseline" which in my head should be 2.73, then add the tires back and somehow obverse the "change" the tires made to that 2.73 ratio when in fact there cannot be a baseline ratio without a tire because the car cannot move, as you said, so there is no "change" to observe until you change the size of the tire

however, to further taunt myself with more theory, going back to the "no wheel baseline" if you raise the rear tires off the ground, put the car in low gear and let off the brake, the tires will effectively be removed from the equation, the RPMs will climb and so will the MPH, if you record the MPH at say 1000 RPMs I have no idea what that would be but probably absurdly high for any practical use in this equation, but anyhow! could you use that as a baseline, then drive the car at 1000RPMs in low gear and record the MPH which should be around 12MPH, could you theoretically use this to calculate what a tire does to a gear ratio?

I know this wouldn't work, because the MPH will be so far off from the RPM it in effect removed another important variable, the gears in the car more or less have no values what so ever, unless there exists a tire with a real value, which leads me to another problem I have with the "effective gear ratio" calculations, since it is only a comparison then the concept is misleading, again I will use my racecar as an example, 26.9/27.4x2.73=2.68 that 2.68 makes me feel comfortable, like I have a real value and I can say "I have a 2.68 gear in my car" but thats only half the story and you have to add the caveat "effectively", because if you change that "old tire" value to something arbitrarily like 17, you will get a new effective value of 1.69.. then all my hopes and dreams get shot to hell, maybe I am getting too involved in this.. though its 5am so there is one excuse

I know I seem to be running in circles.. or maybe spinning my wheels? I love terrible puns, but I am just trying to help explain whats going on in my head

 

[Mike P]

“....the engine/transmission/differential AND tires all need to be accounted for....”

This is absolutely correct. Maybe this will help. You HAVE to start with some base line, and at LEAST one thing has to be a constant to built the rest of the constants on.

I have built a lot of cars over the years and this is pretty much the process I go thru:

Step 1: Determine what engine you’re going to be using and what the car is going to be used for. If it’s going to be a street car what is its most efficient operating RPM, if a race car what is its RPM capability/peak HP and Torque RPM......The RPM range has now become a constant.

Step 2: Determine Tire size. Depending on the body you are using or the sanctioning body requirements, you are going to be limited by either what looks “right” to you on the car or a maximum tire size allowed. Generally speaking you can go up or down a size or 2 from that for fine tuning, but you will be working within a relatively small range that will have only minimal effect on the overall outcome. At this point your tire size has now become a constant.

Step 3: Determine the transmission type. Generally it will be either be a stick or automatic (if it’s an automatic then you will need to take into account for some convertor slippage) and either 1:1 or overdrive. The transmission ratio has now become a constant.

Step 4: This leaves the gear ratio in the differential. As you already have the 3 constants, this is the simple one to figure out. All you have to do is determine the right gear set to keep the engine in its happy place.

 

[Intragration]

however, to further taunt myself with more theory, going back to the "no wheel baseline" if you raise the rear tires off the ground, put the car in low gear and let off the brake, the tires will effectively be removed from the equation, the RPMs will climb and so will the MPH, if you record the MPH at say 1000 RPMs I have no idea what that would be but probably absurdly high for any practical use in this equation, but anyhow! could you use that as a baseline, then drive the car at 1000RPMs in low gear and record the MPH which should be around 12MPH, could you theoretically use this to calculate what a tire does to a gear ratio?

No, the reason you can't do this is because you've removed important variables from the equation that you wouldn't normally remove, the weight of the car, the resistance of the tire rolling, aerodynamic drag, etc. I still see what you're trying to get at, but I think you're confusing yourself by overthinking it. What you just did was try to compare the car on the road versus with the wheels off the ground. You're still trying to COMPARE. The very nature of a baseline and a comparison with that baseline is what it seems you're trying to eliminate, and yet you bring up comparisons to illustrate. The reason you're doing this is that you're trying to mentally compare, but you're trying to do it without comparing. If you want a baseline, drive the car the way it is. That is your baseline. There is no number associated with it, other than the actual, overall gear ratio. That IS the number you're looking for. There is NO tire factor, no "current tire size modifier" if you're not going to compare with another tire size, because it doesn't MATTER. If you were on a desert island, just you and your car, and there were no other tires, no other axles, no other transmissions, would it even matter? Let's say an alien comes along that had never seen a car, and it gets in your car and drives it with 50" tires, would any of the gear ratios or the tire size matter? Not really, because your car with 50" tires would be the only frame of reference. Now let's say you come along and tell the alien that you have a set of 27" tires he can try. You put those on, and the alien says "whoa! That's a lot quicker now!". THEN you can explain that the shorter tires give the car better mechanical advantage, COMPARED with the 50" tires. But until there is a comparison, to the alien, the car with the 50" tires just "is".

which leads me to another problem I have with the "effective gear ratio" calculations, since it is only a comparison then the concept is misleading, again I will use my racecar as an example, 26.9/27.4x2.73=2.68 that 2.68 makes me feel comfortable, like I have a real value and I can say "I have a 2.68 gear in my car" but thats only half the story and you have to add the caveat "effectively", because if you change that "old tire" value to something arbitrarily like 17, you will get a new effective value of 1.69.. then all my hopes and dreams get shot to hell, maybe I am getting too involved in this.. though its 5am so there is one excuse

No, and again, I think you're getting the math backwards. the 17" tires compared with the 27" tires would be HIGHER numerically, they would give MORE mechanical advantage. Without checking your math, maybe the effective gear ratio would be 1.69 if you went FROM 17" tires to 27" tires. But going from 27" tires to 17" tires would make your effective gear ratio more like 4:30...again, just a number out of the air, I didn't do the calculation. But to get a baseline, a real number, if you took your car exactly as it is now, without referring to RPMs or accelerometer numbers, the answer to your question, the number you are looking for, is "yes". Add another tire size to be factored and then we can talk about numbers. Without numbers to be compared, there can be no comparison.

 

[billyjack]

I turn wrenches for a car with no transmission and a quick-change rear gear. Most of our right rear tires are about 104" in circumference. If we have an unusually large or small tire on the rack, I just solve this equation (using a 102" circ. and 5.56 gear for this example):
104/5.56 = 102/G where "G" is the new gear you need
cross-multiply to solve: 104 x G = 5.56 x 102 =567.12
divide both by 104 to solve for G
567.12 / 104 = 5.49 = G
so we'd change to a 5.49 gear to keep rpm's the same with a smaller tire.
It's a simple equation you can do quick at the track. I use the same equation to do other things like determining what speedo gear you need if you change gear ratios or tire sizes on a street car. It'll work in any case where the relationship is linear.

Bill

 

[ReQ]

No, and again, I think you're getting the math backwards. the 17" tires compared with the 27" tires would be HIGHER numerically, they would give MORE mechanical advantage. Without checking your math, maybe the effective gear ratio would be 1.69 if you went FROM 17" tires to 27" tires. But going from 27" tires to 17" tires would make your effective gear ratio more like 4:30...again, just a number out of the air, I didn't do the calculation. But to get a baseline, a real number, if you took your car exactly as it is now, without referring to RPMs or accelerometer numbers, the answer to your question, the number you are looking for, is "yes". Add another tire size to be factored and then we can talk about numbers. Without numbers to be compared, there can be no comparison.

I was comparing the 17 as the old tire, going from the small 17" to the larger 27.4"

I do have a habit of over thinking seemingly simple things, usually when it involves math.. I hate so many things in math, like the "numbers paradox" the fact that there are as many even (or odd) numbers as there are whole numbers, the reason its hard for humans to fully come to terms with such a concept.. is because we cannot fully comprehend infinity, if there is an infinite amount of whole numbers there will also be an infinite number of even and odd numbers, this is somewhat relevant to this topic, it explains why I have a hard time dealing with the fact that there is no value until you have a comparison, it feels almost like without a different size tire to compare to there is no value, and the concept of something having no value is hard to truly understand, especially when there are so many other values involved that you can equate, having a value be meaningless without something to compare it to is a simple concept, but when you say that you can only compare this value, to another value that replaces it, this get complicated in my head, basically saying the original value had no value until it was changed

I am basically trying to divide by zero in essence, though its more complicated than that in this case, but still no more possible


by the way, I LOVE winged sprint cars, they rarely come to our track but when they do its amazing to watch them, they get off the corners so fast its mind boggling, some of them pull the left front tire down the straights, ridiculous torque lol I want to drive one so bad