# NP formula

#### giannip

##### New Member
Hi

Could one of the brainier members of this forum post the AP to NP formula if possible ?

Can't seem to find it...

#### frenchyge

##### New Member
To find Normalized Power over a duration of 5 minutes or longer:

1) starting at 30 seconds, calculate a 30 second rolling average for power​
2) raise the values obtained in step 1 to the 4th power​
3) take the average of all the values obtained in step 2​
4) take the 4th root of the number obtained in step 3​
Source: Training and racing using a power meter: an introduction -- Andrew R. Coggan, Ph.D.​

#### Yojimbo_

##### Well-Known Member
Just to continue this in a slightly different vein......

Anyone know why it's to the 4th power and not something else? I'm curious as to the basis for this.

#### giannip

##### New Member
Thanks everyone. I was loking for the ACTUAL formula. As in all the funky mathematical stuff

#### Alex Simmons

##### Active Member
frenchyge said:
Is the 4th order discussion in there?
No. Brain fade on my part.

#### frenchyge

##### New Member
giannip said:
Thanks everyone. I was loking for the ACTUAL formula. As in all the funky mathematical stuff
There is no formula, funky or otherwise, to convert AP to NP. You have to independently find NP based on the power data from the ride, using the steps I posted above. For some rides, NP will equal AP, and on other rides it will be higher or even much higher. There's a spreadsheet in the files section of the Wattage Google group that will calculate it for you if that's what you need.

#### frost

##### Member
frenchyge said:
There is no formula, funky or otherwise, to convert AP to NP. You have to independently find NP based on the power data from the ride, using the steps I posted above. For some rides, NP will equal AP, and on other rides it will be higher or even much higher. There's a spreadsheet in the files section of the Wattage Google group that will calculate it for you if that's what you need.
Just came to my mind from this question something that I have been thinking recently:
Does someone have a simple formula to calculate NP for a (theoretical) square profiled interval/repetition session giving a few parameters like interval time, interval power, recovery time, recovery power and total number of intervals. I could easily write a progam for that but it would be nicer to have a spreadsheet solution to play with numbers when planning interval sessions.

#### frenchyge

##### New Member
I'm sure there are nicer ones out there, but this is the one I use. NP and TSS values are approximate since smoothing is neglected.

#### giannip

##### New Member
frenchyge said:
There is no formula, funky or otherwise, to convert AP to NP. You have to independently find NP based on the power data from the ride, using the steps I posted above. For some rides, NP will equal AP, and on other rides it will be higher or even much higher. There's a spreadsheet in the files section of the Wattage Google group that will calculate it for you if that's what you need.
so there IS a formula how else would CP calculate NP for a ride ?

or am I being daft again

#### giannip

##### New Member
frenchyge said:
I'm sure there are nicer ones out there, but this is the one I use. NP and TSS values are approximate since smoothing is neglected.
thanks

#### daveryanwyoming

##### Well-Known Member
giannip said:
so there IS a formula how else would CP calculate NP for a ride ?...
Well there's definitely an algorithm or a defined sequence of steps and they're exactly what frenchyge posted above. It's a bit harder to express that algorithm which operates on a list of data values as a closed form expression. It can be done with time indexed summations but it won't look like high school algebra because of that nasty 30 second averaging window.

But for a fairly simple closed form expression you could use:

NP = (mean(psmooth^4))^0.25

where:
- psmooth is the time series power data smoothed with the 30 second sliding window function described by frenchyge in step 1. and the function "mean()" is the linear averaging of all values enclosed in the parathenses.

In the case of frenchyge's spreadsheet the smoothing function is ignored which works fine for blocked style workouts where each block of a different power is much longer than 30 seconds. I use the same sort of spreadsheet for workouts on gym ergs where I hold a given power for 5 minutes or more.

You can code the full smoothed version in a spreadsheet, it just forces you to enter data at a much finer resolution with at least a data point every 15 seconds or better yet at the actual power meter recording rate which makes for a lot of hand entry into a spreadsheet if you're not reading the files directly from your PM.

-Dave

#### frenchyge

##### New Member
giannip said:
or am I being daft again
I'm beginning to wonder...

There's no formula for converting AP to NP. Cycling Peaks WKO+ determines NP by putting the point-by-point power data through the steps described in post #2. A spreadsheet will do this quite easily, but you have to know the complete data stream to feed into it -- AP alone is not enough info.

To illustrate:
if I have a 1hr ride where I averaged 250w, there's no way to use that information to determine the NP of that ride. There are a multitude of ways to end up with an AP of 250w, (ie, 30 min at 300w + 30 min at 200w, 15 min at 300w + 45 min at 233w, etc.) and they will all have different NP's.

To determine NP, you have to know exactly what was done during the ride. The NP of a steady 250w ride is very different from a ride consisting of 300w intervals with 200w rest periods.

Hope that helps explain, but maybe I'm not understanding exactly what you're looking for.

ok I get it now.

Thanks!

#### frost

##### Member
frenchyge said:
I'm sure there are nicer ones out there, but this is the one I use. NP and TSS values are approximate since smoothing is neglected.
Thanks. That's pretty much like what I use. I was just wondering if the smoothing could be applied somehow in a formula.

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