Tuesday, January 13, 2009

Quadrant Analysis

Earlier I posted about a thought I had - to do a Quadrant Analysis (QA) on the power meter data from my Threshold Tolerance Intervals (TTIs), comparing TTIs done at my local training ground, Centennial Park Sydney, to TTIs done on my home trainer, Thunderbird 7.

Funny, in the several years I've been posting about power meter stuff, I haven't mentioned QA. Yet it is one many funky tools to help explain some the differences in the physiological demands of different types of rides.

I don't really have to go into much detail to explain it, since it's already been done by Dr Andrew Coggan and you can read all about it here.

But the short version is that QA is useful for examining the neuromuscular demands of a ride. Essentially it plots pedal forces versus pedal speed (the combination of both equaling power) for each data point recorded by the power meter. In this way, we can not only see how much power we produced during a ride but also gain additional insight into how we produced that power.

There are a number of ways such a plot can be used (e.g. examining and/or comparing ride data with your maximal pedal force-pedal velocity relationship) but I'll leave that for another day.

OK, so the plot is shown above. Let me run you through it:

- The vertical axis is Average Effective Pedal Force (AEPF - measured in Newtons)

- The horizontal axis is Circumferential Pedal Speed (CPV - measured in metres per second)

- Plotted in little red and blue dots/circles are the AEPF and CPV for each second of power recorded by the power meter. The data is from the "on" parts of my intervals only, that is just the time I spent at the intended effort. There is 40-minutes of data for each group.

- The green curved line shows the point at which pedal forces and pedal speeds, when combined, equal my Functional Threshold Power.

- the vertical and horizonal purple lines delineates the quadrants and represent 90rpm (with a 175mm crank) and 167 Newtons (or the same as applying a force of ~ 17kg).

The four quadrants represent:
I - high pedal speed & high force (e.g. sprinting at high speed)
II - low pedal speed & high force (e.g. hard efforts, such at track starts)
III - low pedal speed &low force (e.g. just noodling along at low rpm)
IV - high pedal speed & low force (e.g. spinning fast but easy downhill)

We plot AEPF and CPV, since from a neuromuscular point of view, what's important is both the force and speed of muscle constractions/movement. Investigating either AEPF or CPV in isolation from the other is a fairly pointless exercise. (Refer Pithy Power Proverb "Cadence is a Red Herring" - R. Chung).

We can only plot AEPF, since each point of power meter data covers one or more revolutions of the cranks, in other words, the average of the forces applied to the pedal for an entire rotation of the crank. What this doesn't show is the variability in forces applied around the various points in the crank's revolution. As we know though, the greatest forces are applied on the downstroke, and by a happy coincidence, the maximal force exerted on the downstroke by each leg is roughly double the AEPF*.

* post edit: it was pointed out to me by Robert Chung I had expressed this relationship incorrectly (I had said "the maximal force exerted by one leg is the roughly the same as AEPF") and made this correction to show what I originally said as well as what it should have said.

CPV is basically similar to pedalling cadence, so why don't I just show cadence instead, since most people can related to what 90 rpm is like? Well in this case, the crank length on each bike is different. On the road bike I have 175mm cranks and on T7 I have 170mm cranks. So at the same cadence, the CPV would be higher on the bike with longer cranks. Or for the same CPV, my cadence would be slower on the bike with longer cranks.

If however you were examining ride data from rides using the same length cranks, then certainly you could also show cadence.

OK, so what do we make of the plots of my TTIs?

Well the first thing is that the dots are quite tighly grouped near the centre of the chart, which is pretty typical for efforts of a time trial nature. Generally the flatter the terrain, the more tightly grouped the dots will appear for a quasi-steady state effort. This contrasts significantly to plots for track races, criteriums and rides over hillier terrain, where the dots are widely scattered around the chart. In rides like MTB, the technical nature of riding can see a rider bumping up towards their maximal AEPF-CPV curve quite frequently.

The next thing is how much more tightly grouped the blue dots (indoor trainer) are compared to the red dots from the outdoor ride in the park. This shows that while the average power from these efforts was very similar, there were still differences in how I produced that power in each case.

We can see that the dots are close the the green line (denoting a pedal force/speed combination at FTP) and that the effort, overall on average, was just below my FTP.

The red dots tend to parallel the shape of the green line, which is reflective of me seeking to maintain power within a desired band over slightly variable terrain (I think the total altitude change is ~ 16-18 metres over the course of a 3.8km loop, with a few ups 'n' downs along the way). My speed varied significantly with the terrain and my cadence varied as well, although not by as much as speed since I would change gear regularly.

So, when riding on a trainer, there is a tendency for the AEPF-CPV relationship to show more of a rifle like plot during such Threshold Tolerance effort, whereas outdoors on more variable terrain (and conditions) the plot looks a little more like it came from a shotgun, albeit it one with an odd shaped barrel!

Is it important?

Well it simply serves to show that similar efforts can have variable neuromuscular demands and even changes as small as this may affect the power one is capable of producing in a given scenario. It just emphasises the specificity principle.

If your time trials are outdoors, makes sure you do some time trial training outdoors and ensure your legs are ready for the more variable neuromuscular demands.


Robert said...

the maximal force exerted on the downstroke by each leg is roughly the same as the AEPF

I'm not sure this is right. I think max force is roughly twice average force. At least, that's what the Kautz pedal force data show.

Alex Simmons said...

Yup, got it, thanks, and have made a post edit accordingly.

Matt said...

Hi Alex - just wanted to drop a note and say that you do a great job of communicating the myriad of little things that come with power training. I like the recent tie n with the indoor/outdoor power discussion from the wattage list...very nice. I am a coach in Northern California and you are one of my regular reads...

all the best