1001 replies to this topic

[Steve Scheifler]

Bench, I wasn't suggesting, or thinking you were suggesting, anything about a lighter flywheel for actual weight reduction. The stuff you quoted attempts to make the physics more "accessible" (hate that term) by equating it to reducing weight rather than increasing power. Just another way to think about the benefits in terms of acceleration, but I think not really helpful. And it isn't that the benefit falls at higher ENGINE RPM, (quite the opposite in fact), but rather that it falls off as the *rate of change* in RPM decreases. It's all about the length of time available to achieve a fixed amount of work.

Tom, if you can do the math on the theoretical benefits of shaving roughly 2.5 lbs from the outer circumference of the 1.6 flywheel, please take the time to do so and we can compare results. I've been working on it and that's why I requested some 2nd gear data in another topic (no luck), but I don't claim to be qualified to swear the results will be accurate in absolute terms. I "know" how it works and the approximate scale much as I know that cooler intake air provides the porential for more power. I've also followed arguments about it more than once and reviewed the math and concluded for myself who had it right. But what I will offer in this case still relies on the assumption that someone else's basic calculations of joules are correct and that how I then apply them is valid. Any and all help in determining the true value of proposed changes is welcome.

[Tom Hampton]

Alright. I'm pretty busy these days, but let me think about it a bit.

[RWP80000]

"Bench, I wasn't suggesting, or thinking you were suggesting, anything about a lighter flywheel for actual weight reduction. The stuff you quoted attempts to make the physics more "accessible" (hate that term) by equating it to reducing weight rather than increasing power. Just another way to think about the benefits in terms of acceleration, but I think not really helpful. And it isn't that the benefit falls at higher ENGINE RPM, (quite the opposite in fact), but rather that it falls off as the *rate of change* in RPM decreases. It's all about the length of time available to achieve a fixed amount of work.

Tom, if you can do the math on the theoretical benefits of shaving roughly 2.5 lbs from the outer circumference of the 1.6 flywheel, please take the time to do so and we can compare results. I've been working on it and that's why I requested some 2nd gear data in another topic (no luck), but I don't claim to be qualified to swear the results will be accurate in absolute terms. I "know" how it works and the approximate scale much as I know that cooler intake air provides the porential for more power. I've also followed arguments about it more than once and reviewed the math and concluded for myself who had it right. But what I will offer in this case still relies on the assumption that someone else's basic calculations of joules are correct and that how I then apply them is valid. Any and all help in determining the true value of proposed changes is welcome. "

 

Steve,

Can you use read AIM "*.drk" files to pull the data you are requesting?  If so I can send you files from our 1.6L car.  If you can,  PM me your e-mail and I will send you some data.

 

Rich Powers

[Jim Drago]

Jim, you in the mood to bust balls, bust the balls of the SMAC for their thought of decreasing the flywheel weight by two (2) pounds. There are guys on this site who talk about reducing their tire weigh and it isn't to have less un-sprung weight.

Not sure I could be more clear? I sent a letter in favor of all four changes.. The Flywheel is a waste of time, but if you and others want to do it, I have no issue with it being allowed. I have had conversations with the main proponent of the flywheel on the SMAC and told him the same thing As far as busting balls, usually yes. But in this case just agreeing with what I feel is common sense in Steve's post.

[Tom Hampton]

Steve-

 

I did some quick calculations in the energy domain just to see what makes "sense", and answer a 2 simple questions:

 

1.  How much kinetic energy does the car gain in the useful RPM range of each gear (5000 - 7200 rpm)?

2.  How much kinetic energy is added to the flywheel ring across this range? 

 

The theory being, if the energy isn't absorbed by the ring, then it is available to be used to accelerate the car.  Obviously there is more math to translate this energy into an effective torque or power change.  At the end of the day, you won't do BETTER than whatever these numbers suggest...only worse.

 

In round numbers the weight being proposed for removal gains about 2000 joules of energy between 5000 and 7200 rpm. 

 

In each gear the car gains the following Kinetic energy amounts from 5000 - 7200 rpm:

 

1st      67   Kjoules

2nd     185 Kjoules

3rd      373 Kjoules

4th      660 Kjoules

5th      997 Kjoules

 

So, by lightening the flywheel in the area specified you have freed up 3%, 1%, 0.5%, 0.3%, 0.2% of the total energy required to accelerate the car in each gear, respectively. 

 

Does that compare similarly with your own numbers? 

[Steve Scheifler]

 

Hey Tom, thanks!  Here is my long-winded version so people who are interested can understand a little more about it or challenge my approach.  I am posting this without first comparing the results to yours.

 

To calculate the amount of energy required to accelerate the flywheel (and the energy stored by it) I am using a convenient online flywheel energy calculator. 

 

http://www.botlanta....c/flywheel.html

 

One thing I like about this one is that it includes output for a uniform "disk" flywheel and also for a "ring" type with all the mass at the perimeter (not possible but gives us an upper limit and proves useful later though it's really just 2x the disk value).  Our flywheel is not a simple uniform disk and in fact one proposal is to remove the "inertia ring" which is at the outer perimeter exactly because it increases MOI (Moment Of Inertia) more per ounce of mass than just making the entire disc thicker.  So neither of the calculations is exactly applicable but they provide a range and using them we can extrapolate numbers that are close enough. (someone with the right CAD software could generate very accurate numbers for us).

 

The calculator inputs are the weight and diameter of the flywheel and the RPM at which it is spinning.  The output is energy in joules (the KE, kinetic energy, Tom mentioned) and inertia. For our purpose I am using the KE number which we can think of as the amount of energy "spent" to spin the flywheel up to the input RPM. We can then convert that to HP simply by dividing it by the known constant of 746 (joules per HP).  The current minimum flywheel weight is 17.6 lbs or 282 oz and the diameter is 11.37 inches. So if we input those values and 7200 RPM we see that it requires 23704 joules or 31.8 HP to get the flywheel up to speed.  Wow, that's a lot!  But, we aren't starting at 0 RPM, not even a dragster does that. We typically start accelerating from something above 5000 RPM and if we fall below that we downshift. So the energy "spent" on spinning the flywheel during a run from 5000-7200 is less than 31 HP, but we can't prorate as a simple percentage because the energy required to spin a disk goes up by the square of the RPM. Fortunately we have a handy calculator so by solving for our "start" RPM and subtracting from the value for 7200 we should have the energy required to spin the flywheel though a given range. If I do that for 5500 RPM (as in a 3rd gear pull) I get 13832 joules or 18.5 HP, which subtracted from 31.8 (the value for 7200) gives us 13.3 HP to cover that RPM range.

 

That still sounds like a lot, and it is, but what we haven't factored in yet is time.  Time is the BIG variable here. Feel free to read up on angular impulse (torque times time) and the torque time graph etc. but for now suffice to say that our calculated HP number can be thought of as "horsepower seconds". In other words if our car could accelerate from 5500 to 7200 in one second then the stock flywheel would be "costing" us approximately 13.3 HP (a bit more because of the non-uniform distribution of weight, but let's keep it simple for now). I don't think even an East Street SM could pull that off in 1st gear, but it illustrates how the numbers work.  Let's say that in 3rd gear on a straight level stretch it actually takes 5 seconds to go from 5500-7200. The energy needed to spin the flywheel hasn't changed but we have spread that "work" out over a span of five seconds, so now the flywheel "costs" 13.3/5 = 2.66 HP throughout the five second run.  (Is this starting to sound like how a typical roller dyno works, measuring how long it takes to spin up a heavy drum?)

 

Not sounding so great anymore is it?  And that's total cost, or what you would theoretically save by eliminating the flywheel entirely. Unfortunately, all else being equal the mass part of these equations is linear so reducing the weight by 2.5 pounds (14.2%) drops the net savings/gain to just 0.38 HP.  In our case the initial joules and HP are probably a bit low because of the shape of the flywheel, and if we take the weight off at the inertia ring then the savings is more like it would be for a ring flywheel.  So I recalculated the cut flywheel as if it were a uniform disc (close enough for our purposes) and then separately calculated the part we are cutting off as a ring (which is exactly the case) and I find that the real total HP for the current flywheel from 0-7200 is 36.2 HP.  Repeating the steps to look at just our typical RPM range of 5500-7200 yields a more accurate current cost of 15.1 HP seconds and removing the ring drops that to 11.3 for a savings of about 3.8 HP seconds. Divide that by the 5 seconds required to accelerate in 3rd gear and you have an effective net savings equivalent to about 3/4 of a HP in 3rd gear.  

 

Based on my data, in 4th gear between T3 and T5 at Road America, which is effectively straight and significantly down hill, it takes about 15.4 seconds to cover the same 1700 RPM, which translates to approximately 1/4 HP "gain" by removing the inertia ring.  One place where 1.6 owners often wish they had a little more torque at Road America is out of T14 and up the hill to start-finish.  Well, because the rate of acceleration is the big variable and the lower it is the less a lighter flywheel will help, it may be a bit of a disappointment because at such a low rate of acceleration it will be like gaining roughly 0.1 HP.  The good news for those who frequent tracks with a lot of 2nd gear corners is that you might actually experience a perceptible bump from the change, but what RPM do you normally drop to in 2nd?

 

If you still think it sounds like a big deal to lighten the stock flywheel, keep in mind that what it really does is store all that energy and every time you upshift it does give some of that back as a little boost to begin the next gear.  You probably didn't even realize that your Miata (and every other car in the world) already has an energy recovery system, but that's what the flywheel is.  The idea is to store energy so taking off from a stop is smoother and easier, but it also pays some back with each shift.  So when you calculate what the flywheel is costing you don't forget to give it credit for that payback.  And, though it may be just fine, don't forget that the front pulley is also an harmonic balancer designed specifically to work with the stock crank, flywheel and clutch.  Make big changes to those and there may be other unanticipated consequences.

[Steve Scheifler]

Tom, I gather that your initial calculations do not attempt to factor in the decrease in the rate of acceleration as a result of aerodynamic drag. Is that true? Would you agree that although it does not change the energy absorbed by the flywheel it does impact the effective equivalent HP loss throughout the gear? In that case, percentages in terms of impact on actual car acceleration would drop of more quickly than the energy numbers might imply.

[Sean - MiataCage]

Tom and Steve.... Thank you both for taking the time to try to put some physics/math/science behind the flywheel mystery.  If I had $1.00 for every person who says something will or won't work but can't back it up with any math I would be racing in F1.  In order for anyone to make an informed decision we have to take the emotion and the authoritarian approach to answering some of these questions and use some physics/math/science.  It will only make us all that much more informed to come to our own decisions.

 

Now if we could just recover those darn Hillary e-mails

 

Thanks for taking the time to do this.

Sean

[Andy Mitchell]

Not saying I really know anything, but I teach Mechanical Engineering and Steve's basic approach seems to make sense to me. Except that 1 hp does not equal 746 joules, it equals 746 joules/sec, but he fixes that when he factors time for each acceleration run in later on.

 

Take away for me is that it's hard to know for sure what benefit might actually be achieved by lightening the flywheel (if any). There are a lot of assumptions and variables at play in the calculations. One thing is for sure, the 'changes' will be different from track to track, according to exactly what the pulls in the various gears look like.

 

I still like the header idea...

[Steve Scheifler]

Andy, you are right of course. I left time out initially to keep it simple to follow the energy part and because it produces numbers similar to where many people seem to land when doing this through various approaches based only on weight and gearing. They get results that sound pretty good, and sells flywheels, but fail to account for the single biggest real-world factor, time. I wanted that emphasized so I applied it last. Think of it as a teaching technique.

[Tom OPM]

Tom and Steve thanks for taking the time to try and make sense of all this for the rest of us non engineering types. So unless we do a lot of 1st and 2nd gear pulls on the track the gain would probably not be noticed ? From my own background I also remember the lighter flywheel can also hurt top end in 4th and 5th gear. The lightened unit does not store energy like a heavier unit ?

[Tom Hampton]

Tom, I gather that your initial calculations do not attempt to factor in the decrease in the rate of acceleration as a result of aerodynamic drag. Is that true? Would you agree that although it does not change the energy absorbed by the flywheel it does impact the effective equivalent HP loss throughout the gear? In that case, percentages in terms of impact on actual car acceleration would drop of more quickly than the energy numbers might imply.

Correct. That was exactly my point in saying the above was best case.

[Steve Scheifler]

I figured, but wanted to spell it out and tie it back to my numbers just to be clear that time is the main difference, so even though at a glance our numbers are different they are actually close and agree on the approximate scale of the benefits. Thanks again for taking the time to crunch core numbers for comparison, I wouldn't expect anyone to trust a single source, especially when it seems to defy conventional beliefs.

[Andy Mitchell]

Tom, did you account for all the rotary energy tied up in the drivetrain and wheels when you calculated your KE numbers? It's generally pretty significant, and would tend to reduce your percentage gains even more.

 

Incidentally, shaving your tires accomplishes something similar to shaving flywheels in the grand scheme of things... except it normally happens at lower rotational speeds.

[Steve Scheifler]

Tom and Steve thanks for taking the time to try and make sense of all this for the rest of us non engineering types. So unless we do a lot of 1st and 2nd gear pulls on the track the gain would probably not be noticed ? From my own background I also remember the lighter flywheel can also hurt top end in 4th and 5th gear. The lightened unit does not store energy like a heavier unit ?

On the first part, true, great for drag (conditionally and within limits) and autocross, not so much for us. As for the top end, I've heard/read that before but can't say I see how the physics support it actually going negative while still trying to accelerate. I'm not saying it isn't possible, I just need a better explanation. But regardless, I don't see how it would amount to much either way. As we debated some months back, by the time you get to 5th gear each HP or lb/ft is worth dramatically less thanks to the double whammy of reduced torque multiplication of the gearing and the air resistance increasing at the square of velocity. That's why you can go 100mph in a given car with maybe 60hp but to go 200 would take a LOT more than 120hp. That's also why a few extra peak HP for the 1.6 isn't suddenly going to make them overdogs on long straights, their real advantage in those cases is not engine power it is holding 4th a bit longer due to the higher redline. The drop in torque multiplication is delayed, giving them a brief advantage.

[James York]

This makes my head hurt.  Now I am sure i made the correct choice in my education by choosing the chemical engineering discipline.

[Tom Hampton]

To elaborate, I took the age-old  "assume the miata is a point mass, operating in frictionless space" approach to simply determine an upper bound for the percent improvement.  I also rounded some of the numbers to make the calculations easier, since i elected to do them by hand (I rounded the ring mass to 2.2 lbs => 1 kg, and the miata mass to 2200 lbs => 1000 kg).  Frankly, I took this approach for selfish reasons, I wanted to know if it was even worth bothering to go further in the analysis.  I think the numbers above make it clear.  There is less than 1% benefit in gears 2-3, and less than 1/4% in 4 and 5. 

 

No, I didn't take into account the Kr of the wheels.  The moment of inertia of the wheel structure is a little more involved to calculate (a 3-4 component, piecewise construct would be sufficient).  As you point out, these only serve to reduce the real benefit.  So, unless the scale of the ideal case (above) were about an order of magnitude higher, its really not worth the trouble. 

[Tom Hampton]

This makes my head hurt.  Now I am sure i made the correct choice in my education by choosing the chemical engineering discipline.

 

Funny.  I feel exactly the same way about Chemistry-- crazy voodoo science that.

[Steve Scheifler]

Tom, did you account for all the rotary energy tied up in the drivetrain and wheels when you calculated your KE numbers? It's generally pretty significant, and would tend to reduce your percentage gains even more.

Incidentally, shaving your tires accomplishes something similar to shaving flywheels in the grand scheme of things... except it normally happens at lower rotational speeds.

True about tires, and driveshafts etc. But, anything after the trans is different in that it spins up much more gradually in direct proportion to car velocity so the time factor is amplified compared to the engine which changes speed relatively quickly and then repeats the toughest part for each gear. Not to say lighter wheels and tires don't count, they do. The diameter is large, which is a big factor, and of course there are four of them, but you can't directly compare them pound for pound with the flywheel. The other popular part to swap is the driveshaft. When you consider the diameter, weight, and being after the trans, it's hard to see why anyone would risk getting caught with a slightly lighter one.

[38bfast]

Steve, Tom, thanks for all the work. As you have described there is a exponential cure created in hp as the speed increases. Starts out high and flares flat. There is also a simaler shaped curve that oposes via drag of the car. These curves typicaly cross at about 65 mph in our style cars. So above 65 mph you are not fighting mass you are fighting drag vs hp.