Where does power come from?

[Fday]

So, from your perspective:

Oxygen is not an element.

Asprin and Morphine are modern drugs.

All IUD's are dangerous due to purchased trials.

All modern clinical drug trials lead to dangerous drugs because the researchers are accepting payola.

Thus proving that paying people to study your PCs would be wrong.

No, oxygen is an element, O2 (inconcentrations above atmospheric) is a drug.

Aspirin and morphine are modern drugs. For some of the things they do there is no better alternative (baby aspirin for preventing heart attacks, relieving pain).

And all drugs are dangerous, clinical trials, paid or otherwise (they are all paid as it is the manufacturers job to prove they are safe and efficatious to the FDA if they want them to be licensed for sale, that isthe way it works) are imperfect at finding all the risks (and benefits) even though the law states the FDA cannot license a drug unless it is found safe and effective. "safe and effective" is always relative when it comes to anything in medicine or, even, in life.

Cheers.

Frank

 

[Fday]

The drugs work as expected. There is just a human nature problem. For some reason sane humans think that a drug or device should not harm anyone. When it starts to link to 100 or so deaths, they get pulled.

My mother is still on a Cox2 inhibitor (if that is the correct way to describe it) that will not be prescribe by a doctor to a new paitent. Her doctor has tried to take her off of it a couple of times. She may have found a new drug to substitute for it finally. But until now my mother, myself, and her doc. have all discussed the side effects. My mother decided she would rather take the risk then live with the pain she was in without the drug. So yes, you would probably not be on the drug, but that does not mean the drug is not effective.

Likewise, she when through another drug treatment that has been determined safe. It turns out there were side effects with her other medications. The drug that caused the side effect did its job, it is just the tests are not fail safe. The drug manufacture will hopefully test for these side effects.

The brest implant issue has since been determind to have not caused the problems once thought. Yes they leaked, but now it appears Dow was put out of business by a bunch of lawyers that were wrong.

As for your product, I think it would be safe to say after you had the research completed. Not everyone would see the same results. Some would see more, some would see less. That is to be expected.

However, people would not really care because mostlikly people would not die.

Actually, we have had several customers die while using our product. They were all hit by cars while out riding. In all the instances (except one where we refunded the money to the spouse) I believe the PC's were given to riding buddies by the surviving spouse. Life is dangerous and unpredictable.

 

[vadiver]

Actually, we have had several customers die while using our product. They were all hit by cars while out riding. In all the instances (except one where we refunded the money to the spouse) I believe the PC's were given to riding buddies by the surviving spouse. Life is dangerous and unpredictable.

So what do either of your last two posts do with paying a research firm to test your hypothosis that your product improves power output for the typical rider by 40% in each of two years?

 

[Fday]

So what do either of your last two posts do with paying a research firm to test your hypothosis that your product improves power output for the typical rider by 40% in each of two years?

You misrepresent the claim and those last posts have little to do with this other than the fact that no study proves or disproves anything. Plus, it is not always necessary to have a study to prove something actually works for it to be true. Morphine has been used as an effective treatment of pain for over a 1000 years or so and not a single study to demonstrate the benefits until lately. Morphine has been used since before the scientific method was developed. And, it is still pretty much the best available despite the fact that there might be other newer drugs that have fewer side effects.

Whatever we were to do studywise people like yourself would criticize the study and proof pretty much until doomsday. So be it.

 

[n crowley]

Sure, for the exact same effort (calories burned) the rider with the larger GE has more power. I think you said something about what riders with more power tend to do, but I forget.

Frank, if you have two riders of equal size, weight and fitness ability in a seated sprint, one uses the PC pedaling technique while the other is a stomper, who will be the winner.

 

[beerco]

they are all paid as it is the manufacturers job to prove they are safe and efficatious to the FDA if they want them to be licensed for sale, that isthe way it works

Which was my original point exactly:

Every medical device in the U.S. today was proven through clinical trials paid for by the manufacturers. The docs are paid per patient to implant/use the stuff and report their results in peer review journals.

[snip]

It's the way it's done

Does this mean you'll put up the cash for some critics to study your cranks?

I wonder why the system is set up that way? It probably has nothing to do with a long history of quacks pushing their products (drugs or devices) whether they work or not do you think?

 

[vadiver]

You misrepresent the claim and those last posts have little to do with this other than the fact that no study proves or disproves anything. Plus, it is not always necessary to have a study to prove something actually works for it to be true. Morphine has been used as an effective treatment of pain for over a 1000 years or so and not a single study to demonstrate the benefits until lately. Morphine has been used since before the scientific method was developed. And, it is still pretty much the best available despite the fact that there might be other newer drugs that have fewer side effects.

These are claims you have made in this thread. Do you want me to find where your have made such claims? All it will do is make you look more the fool.

You are correct, a study will not prove that 100% of the time will the results be the same. That is what the confidence interval represents. For example lets say you commision your study with a 95% CI. Then the hypothosis is confirmed true. At that point anyone should be able to grab 100 typical cyclists and 95 of them would meet your claim.

In the medical industry their tests are to see if the drug does what it is supposed to do, cure ARMD. They also test to see if it is safe. Since there are millions of combinations of drugs out there they cannot test everything. So after release there is a potintial that the drug may kill people. At that point more testing is done and the drug, if it does kill people, will be pulled.

Whatever we were to do studywise people like yourself would criticize the study and proof pretty much until doomsday. So be it.

Not if the study was done properly. I do not think anyone has criticized the two studies that you have the abstracts posted on. I criticize your representation of the studies. It appears others that have made comments on the studies have been along the same lines.

The GE study is fine. It shows that a person does not need to consume as much food while they ride with your product. It does not show they are any more powerfull.

The other study shows that the training program the riders were on, using your product, did improve by 10% or so. This is not the 40% you claim. Further, without the control one cannot conclude that the improvement was from your product. Now a control would not necessarily be needed if a similar study was conducted without your product. Then we would know how much improvement is done solely by training. That is not easy to do, nor is it generally accepted unless there have been a lot of tests done that yeild the same results.

You have provided nothing to support your claims. The only data you claim to have you do not know who gained what/when which leaves that less than creditable. The way you calculate percentage improvement leaves you less than creditable.

 

[Fday]

These are claims you have made in this thread. Do you want me to find where your have made such claims? All it will do is make you look more the fool.

the only claim I make is that our typical new user will gain 40% in power in 6-9 months. The fact I expect that some will see similar gains the second year is not a claim that I expect everyone, or even most, will see those same gains.

Not if the study was done properly. I do not think anyone has criticized the two studies that you have the abstracts posted on. I criticize your representation of the studies. It appears others that have made comments on the studies have been along the same lines.

Sure they have. Even I can find criticism in some way with each as no study is ever perfect.

The GE study is fine. It shows that a person does not need to consume as much food while they ride with your product. It does not show they are any more powerfull.

You are free to interpret those results as you wish. Most would not draw that conclusion from that study.

The other study shows that the training program the riders were on, using your product, did improve by 10% or so. This is not the 40% you claim. Further, without the control one cannot conclude that the improvement was from your product. Now a control would not necessarily be needed if a similar study was conducted without your product. Then we would know how much improvement is done solely by training. That is not easy to do, nor is it generally accepted unless there have been a lot of tests done that yeild the same results.

As I said before, while 10% is not 40%, 6 weeks is not 6-9 months. It does not prove the 40% claim but it does not negate it either. And, since we don't have the protocol we cannot know whether their statistics are valid or not, but since it is being done by an experienced group out of Canada I have no reason to doubt the work is good. Do you?

You have provided nothing to support your claims. The only data you claim to have you do not know who gained what/when which leaves that less than creditable. The way you calculate percentage improvement leaves you less than creditable.

Sure I have, but it is all anecdotal or the result of my own, poorly designed, experiment. Certainly no proof in the scientific sense. Why doesn't someone do an experiment to prove my claims wrong, then I would have to revise them. But, until then I have enough to cause me believe they are true so I don't change them. Sorry to let you down.

 

[Fday]

Does this mean you'll put up the cash for some critics to study your cranks?

I wonder why the system is set up that way? It probably has nothing to do with a long history of quacks pushing their products (drugs or devices) whether they work or not do you think?

No, we don't give cash. But is someone wants to study them and they have a good plan and reasonable protocol we will usually support them with product. We do that all the time. Several university studies are in the pipe line as I write this.

 

[Fday]

Frank, if you have two riders of equal size, weight and fitness ability in a seated sprint, one uses the PC pedaling technique while the other is a stomper, who will be the winner.

If they start out equal, 6 months later the PC'er will win hands down. No doubt in my mind whatsoever.

 

[ric_stern/RST]

If they start out equal, 6 months later the PC'er will win hands down. No doubt in my mind whatsoever.

That'll be the longest sprint ever then...

 

[Carrera]

You need to know your power to weight ration and wattage in these cases. Tyler Hamilton was producing about 430 watts at a weight of 130 pounds. Armstrong can generate close to 500 watts but, of course,he's a bit heavier than Hamilton.
Can bulking up increase your power and wattage?
Jan Ullrich has claimed in the past to have put on a few more pounds purposefully while most people try to lose weight.
Of course, you have to calculate how the cardiovascular process will relate to any increase in bulk. I forget how long it takes for an oxygen carrying cell to work around the body doing its job.

Learn to sit in. Bettini does alright and he's not massive. Tactics, tactics, tactics.





No. There is no reason to want to bulk up.



No they don't. If they did bulk up, there is no reason to think that this would lead to them getting better.

 

[vadiver]

the only claim I make is that our typical new user will gain 40% in power in 6-9 months. The fact I expect that some will see similar gains the second year is not a claim that I expect everyone, or even most, will see those same gains..

Seeing as though you like to call out all the pros that use them, I guess that would be a typical new user. And All, Most, Some, or None of them have seen a 40% gain?

Remember this comment the other day you made.

Anyhow. Enjoyed the thread. Suspect you continued to improve for at least 24 months at which time it started to "level out" some.

Frank

Sure they have. Even I can find criticism in some way with each as no study is ever perfect.

It is how the results are used that gets criticized. There is nothing wrong with either of the studies. They just do not support the claims you make. When you try to say they do, you are the one being criticized, not the studies. The people publishing the stuidies do not claim that there only way to achived these results is through the use of your product. If they wanted to make that claim they would either have had to use a control sample or have a lot of data to support not using a control. That is why they do not make that claim.

You are free to interpret those results as you wish. Most would not draw that conclusion from that study.

You drew that conclution yourself. Then you spoted off that fewer calories burned meant more power. Once again, do you ever pay attention to yourself? We know you are totaly deaf to others around you.

As I said before, while 10% is not 40%, 6 weeks is not 6-9 months. It does not prove the 40% claim but it does not negate it either. And, since we don't have the protocol we cannot know whether their statistics are valid or not, but since it is being done by an experienced group out of Canada I have no reason to doubt the work is good. Do you?

I have no reason to doubt what either study said. But neither study supports your claims.

Being one that has trained a lot for various sports at various times. I know that the majority of my improvements are in the first few weeks of training. I am sure there are many studies that would support this as well. To need to take 75% of a year to train to get to the results needed, that is an awfull lot of training.

Sure I have, but it is all anecdotal or the result of my own, poorly designed, experiment. Certainly no proof in the scientific sense. Why doesn't someone do an experiment to prove my claims wrong, then I would have to revise them. But, until then I have enough to cause me believe they are true so I don't change them. Sorry to let you down.

Frank, the anecdotal data you have is complete BS. On your website you claim to have improved 38%, when questioned you said you improved 38% and another improved around 50%.

Then you come up with your data and the results get completly flipped. You further prove your ignorance when you cannot explain why you add 100% to your results to claim your % gain. You were using Frank math, not real math.

It is your responcibility to sponsor the study that will support your claims. Why should anyone spend their own money to support your business?

You have nothing but refuse to accept that. Instead you will continue to lie and misrepresent your product.

I would also suppose the one study that showed the improvement in GE was trying to support your claim of 40% power improvement, and they could not substantiate the claim. That is why they mentioned there was not improvement in power in their abstract.

BTW, earlier you claimed to have a power out put of 500W after using your product for six or nine months. How long was that 500W sustained?

 

[workingguy]

Then you come up with your data and the results get completly flipped. You further prove your ignorance when you cannot explain why you add 100% to your results to claim your % gain. You were using Frank math, not real math.

I'm not a scientist, but I would have to agree with Frank's math here. Based on the assertion that Power vs speed is a cubic function.

P = k (v)^3

at v1, P1 = k(v1)^3

Given that v2 is 25% faster than v1, v2 = 1.25v1

so P2 = k(1.25v1)^3

Divide P2 by P1.

P2/P1 = k(1.25v1)^3 / k(v1)^3
cancel k(v1)^3 from numerator and denominator.

P2/P1 = 1.25 ^3 = 1.95

In analyticcycling, I used 0.0% gradient, all other defaults,
for 10 m/s, P = 182W
for 12.5 m/s, P = 336W

The ratio is 1.84, slightly less than 1.95, so other factors must be used as well in their calculations.

That said, there is a whole nother thread on pedaling circles vs. just pushing down.

 

[Fday]

Seeing as though you like to call out all the pros that use them, I guess that would be a typical new user. And All, Most, Some, or None of them have seen a 40% gain?

I have been through this before with you. I will try again then I am through with answering the same thing over and over.

No, pros are not a typical new user nor is it them to whom the claim is supposed to apply, the typical purchaser, how is that. (actually, the pros purchase them also, we just give them a substantial "sponsorship" discount). Not sure what the pros have seen as they have not reported that to me. We are trying to get some data out of a couple of the National Training Centers in Canada who have been using them for awhile.

It is how the results are used that gets criticized. There is nothing wrong with either of the studies. They just do not support the claims you make.

Sure those studies support the claim. With those increases in only 6 weeks it is not unreasonable to infer further improvement would continue for awhile and 40% in 6 or 9 months could be entirely possible.

When you try to say they do, you are the one being criticized, not the studies.

People who do not understand studies and my product certainly do criticize me for saying what I say. This is the internet after all. I stand by it all.

The people publishing the stuidies do not claim that there only way to achived these results is through the use of your product. If they wanted to make that claim they would either have had to use a control sample or have a lot of data to support not using a control. That is why they do not make that claim.

The people doing those studies are trying to figure out if PC's help the cyclist, over and above traditional techniques, and if so, by how much. These are almost like pilot studies to see if there is a benefit. If there were no benefit there would be little reason to study further. Since there were demonstrated benefits, further study is warranted since 6 weeks is barely enough time to get accustomed to the cranks, let alone see maximum benefit.

You drew that conclution yourself. Then you spoted off that fewer calories burned meant more power. Once again, do you ever pay attention to yourself? We know you are totaly deaf to others around you.

Greater efficiency can mean two things. For the same power one can eat less or for the same number of calories burned one generates more power. I prefer to concentrate on the second benefit as that is what most racers want. You, for some reason, can only see the first benefit. Not sure why.

I have no reason to doubt what either study said. But neither study supports your claims.

Yes they do, see above.

[/QUOTE] Being one that has trained a lot for various sports at various times. I know that the majority of my improvements are in the first few weeks of training. I am sure there are many studies that would support this as well. To need to take 75% of a year to train to get to the results needed, that is an awfull lot of training.[/QUOTE]If you want to get better you gotta do the work. PowerCranks are a lot of work. They clearly are not for you.

Then you come up with your data and the results get completly flipped. You further prove your ignorance when you cannot explain why you add 100% to your results to claim your % gain. You were using Frank math, not real math.

As mentioned before, I suggest talking to a friend who is a math wiz. I stand by my math.

It is your responcibility to sponsor the study that will support your claims. Why should anyone spend their own money to support your business?

No reason unless they want to satisfy an intellectual curiosity. And few universities are "spending their own money" when they do research. They have some money that they can choose for worthy projects that interests them. If someone comes and waves some money in their face they might or might not take the project on. We don't have any money to wave anyhow so you will have to accept that scientific proof of my claims is not there. I accept that. It is one of the reasons why we offer a 90 day moneyback guarantee. You don't have to accept someone else's word on the worth or worthlessness of the product. You can decide for yourself based upon what you have seen and experienced yourself. About 2-3 in 1000 send them back.

I would also suppose the one study that showed the improvement in GE was trying to support your claim of 40% power improvement, and they could not substantiate the claim. That is why they mentioned there was not improvement in power in their abstract.

None of the studies that were done were trying to prove the 40% power increase claim. If they were they would have lasted for more than 6 weeks. They were just trying to see if there was improvement over traditional training. They showed that. I was actually surprised the numbers were as big as they were for such a short period of time. I would not have predicted that before these studies.

BTW, earlier you claimed to have a power out put of 500W after using your product for six or nine months. How long was that 500W sustained?

I did? Where? The largest power I think I have ever seen me do was about 700 watts on a Power Tap climbing a short hill, probably lasted 10-15 seconds.

 

[Fday]

I'm not a scientist, but I would have to agree with Frank's math here. Based on the assertion that Power vs speed is a cubic function.

P = k (v)^3

at v1, P1 = k(v1)^3

Given that v2 is 25% faster than v1, v2 = 1.25v1

so P2 = k(1.25v1)^3

Divide P2 by P1.

P2/P1 = k(1.25v1)^3 / k(v1)^3
cancel k(v1)^3 from numerator and denominator.

P2/P1 = 1.25 ^3 = 1.95

In analyticcycling, I used 0.0% gradient, all other defaults,
for 10 m/s, P = 182W
for 12.5 m/s, P = 336W

The ratio is 1.84, slightly less than 1.95, so other factors must be used as well in their calculations.

That said, there is a whole nother thread on pedaling circles vs. just pushing down.

The other factor that gets involved is rolling resistance, which is not a cubic function. However, at higher speeds, this becomes so small in comparison that it is reasonable to use the cubic relationship as a rule of thumb.

 

[vadiver]

I'm not a scientist, but I would have to agree with Frank's math here. Based on the assertion that Power vs speed is a cubic function.

P = k (v)^3

at v1, P1 = k(v1)^3

Given that v2 is 25% faster than v1, v2 = 1.25v1

so P2 = k(1.25v1)^3

Divide P2 by P1.

P2/P1 = k(1.25v1)^3 / k(v1)^3
cancel k(v1)^3 from numerator and denominator.

P2/P1 = 1.25 ^3 = 1.95

In analyticcycling, I used 0.0% gradient, all other defaults,
for 10 m/s, P = 182W
for 12.5 m/s, P = 336W

The ratio is 1.84, slightly less than 1.95, so other factors must be used as well in their calculations.

That said, there is a whole nother thread on pedaling circles vs. just pushing down.

But that is assuming P=kv^3. Every where I have found the relationship between power and velocity is is represented as P=VR where r=resistance.

This also holds true when plotting a P/V curve. Using values for A/C it looked more linear than cubic.

If Frank's assertion were correct the ration would me much closer to the 95% as claimed.

You can go back to analytical cycling to verify this. Set drag coefficient to 0 to eleminate that resistance. Then set rolling resistance to .0001 (wooden track). There this same 25% increase in speed only changes power by 25%, not 84% or 95%.

If Frank were correct with P=kv^3 it would be consistantly changing with the value of v, which it does not. The next 10% increse in velocity is again different from the 84%.

Where I claim he does not know what he is doing with his math is, the point where he adds 100%.

He says an 11% gain in sped is a 36% gain in power. The way he calclulated it was:

(1.11)^3=1.36 from which he concluded 36% increase in power. Which again once going to AC yeilds at 32% increase in power.

Following your explination of P1/P2 by writing down P=KV^3 I follow that.

 

[n crowley]

Frank, if a rider who already had the perfect circular pedaling style used your PC's, what changes would he experience in his power application technique ?

 

[vadiver]

I have been through this before with you. I will try again then I am through with answering the same thing over and over.

No, pros are not a typical new user nor is it them to whom the claim is supposed to apply, the typical purchaser, how is that. (actually, the pros purchase them also, we just give them a substantial "sponsorship" discount). Not sure what the pros have seen as they have not reported that to me. We are trying to get some data out of a couple of the National Training Centers in Canada who have been using them for awhile.

A new user getting off of the couch would most likely improve substantially using anything. I improved 27% (18 to 23 MPH on the same course) last spring with out doing much of anything. Since that is only speed, how much is that in power?

Sure those studies support the claim. With those increases in only 6 weeks it is not unreasonable to infer further improvement would continue for awhile and 40% in 6 or 9 months could be entirely possible.

They do not support the claim. All they support is the effects of 6 weeks of use. Nothing else. If you want to go on that assumption why not assume an infinite power gain. You can make the same claims.

People who do not understand studies and my product certainly do criticize me for saying what I say. This is the internet after all. I stand by it all.

I understand your product. I understand what the abstracts say. The abstracts do not support a 40% increase in power. The only study to independently test the PC vs training claims a ~10% increase in GE. That is it. The other says there was an ~10% increse in power. But without knowing how the training program was different that is a who cares figure.

The people doing those studies are trying to figure out if PC's help the cyclist, over and above traditional techniques, and if so, by how much. These are almost like pilot studies to see if there is a benefit. If there were no benefit there would be little reason to study further. Since there were demonstrated benefits, further study is warranted since 6 weeks is barely enough time to get accustomed to the cranks, let alone see maximum benefit.

I agree with this statement.

Greater efficiency can mean two things. For the same power one can eat less or for the same number of calories burned one generates more power. I prefer to concentrate on the second benefit as that is what most racers want. You, for some reason, can only see the first benefit. Not sure why.

Because the second one is stupid in terms of this discussion.

If you have a better GE than me because you use your product and I do not. However you can only generate 300W for an hour and I generate 400W for an hour. If the race were based on we each only had 1000K to burn you would win. But since races are not run that way, it is pointless.

This is kind of like the I am fat, but you are ugly, I can diet line. If you have a beter GE than me, who cares, I just consume more calories while riding.

If you want to get better you gotta do the work. PowerCranks are a lot of work. <snip>

I agree. Show me any athlete in any sport that is going to be working on their base for 9 month out of the year. When is their season?

I have said before, I can see some use for your product. I just do not see 40% increase over normal training techniques.

No reason unless they want to satisfy an intellectual curiosity. And few universities are "spending their own money" when they do research. They have some money that they can choose for worthy projects that interests them. If someone comes and waves some money in their face they might or might not take the project on. We don't have any money to wave anyhow so you will have to accept that scientific proof of my claims is not there. I accept that. It is one of the reasons why we offer a 90 day moneyback guarantee. You don't have to accept someone else's word on the worth or worthlessness of the product. You can decide for yourself based upon what you have seen and experienced yourself. About 2-3 in 1000 send them back.

If it takes 6-9 months to see the bennifits why only a 90 day guarantee? Why would anyone return them before 180 days?

None of the studies that were done were trying to prove the 40% power increase claim. If they were they would have lasted for more than 6 weeks. They were just trying to see if there was improvement over traditional training. They showed that. I was actually surprised the numbers were as big as they were for such a short period of time. I would not have predicted that before these studies.

Ok. But the one study that could compare the results of the users vs. non-users specificllay said their was not difference within or between the groups. That would indicate to me they at least looked at it. If there was a significant difference, they would have said so.

I did? Where? The largest power I think I have ever seen me do was about 700 watts on a Power Tap climbing a short hill, probably lasted 10-15 seconds.

I appologize, it was in post 219 of this thread. You said it was the other person that had the 500W. But my question would be the same. For how long was that sustained.

My max wattage went from 260 to 380 if I remember correctly. Hmmm me thinks at the time, I had better confirm this on some others when I decided to try and find some beta testers to see what others would see. I couldn't give them away but I eventually found several to give them a try. Only one person stayed until they could complete the test to the same ending HR and that person I believe improved from 360 to 500 watts (correction, originally wrote 600).

My confusion was this puts your change at 46% and the other person at 38% which contridicts what you claimed earlier.

 

[vadiver]

I'm not a scientist, but I would have to agree with Frank's math here. Based on the assertion that Power vs speed is a cubic function.

P = k (v)^3

at v1, P1 = k(v1)^3

Given that v2 is 25% faster than v1, v2 = 1.25v1

so P2 = k(1.25v1)^3

Divide P2 by P1.

P2/P1 = k(1.25v1)^3 / k(v1)^3
cancel k(v1)^3 from numerator and denominator.

P2/P1 = 1.25 ^3 = 1.95

In analyticcycling, I used 0.0% gradient, all other defaults,
for 10 m/s, P = 182W
for 12.5 m/s, P = 336W

The ratio is 1.84, slightly less than 1.95, so other factors must be used as well in their calculations.

That said, there is a whole nother thread on pedaling circles vs. just pushing down.

I should have thought of this sooner. Look at the units.

Again from what I found power equals work devided by time. Or P=F*V

P in watts. F in Newtons and V in M/S.

Force = M*A so a newton if I am not mistaken would be (kg)*m/s^2
Velocity is m/s.

so a watt would be (kg)*m/s^2*m/s or (kg)m^2 / s^3.

Watt=kgm^2s^-3
Is this correct?