2 road cyclist vs 1 TT cyclist

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warthog1
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Re: 2 road cyclist vs 1 TT cyclist

Postby warthog1 » Wed Sep 21, 2016 11:04 pm

Thanks Alex. :)
My tt set up must be way more aero than the roadie. Much faster on the tt.
Or was. It doesnt get ridden now.

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Re: 2 road cyclist vs 1 TT cyclist

Postby g-boaf » Thu Sep 22, 2016 6:06 am

warthog1 wrote:Thanks Alex. :)
My tt set up must be way more aero than the roadie. Much faster on the tt.
Or was. It doesnt get ridden now.


Or you sit up high on the road bike. That doesn't help. Of course you have to be flexible enough to get lower on the bike. Never under-estimate how much gain you can get by not sitting up and acting like an air-brake.

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Re: 2 road cyclist vs 1 TT cyclist

Postby Calvin27 » Thu Sep 22, 2016 8:55 am

Alex Simmons/RST wrote:My aero difference between each set up was ~ 18%, and so my solo pursuit self would be faster than me and my clone on mass start track bikes.


Haha doesn't matter what configuration, after 2 laps in the front I'm hammered :P
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Re: 2 road cyclist vs 1 TT cyclist

Postby warthog1 » Thu Sep 22, 2016 9:24 am

g-boaf wrote:
warthog1 wrote:Thanks Alex. :)
My tt set up must be way more aero than the roadie. Much faster on the tt.
Or was. It doesnt get ridden now.


Or you sit up high on the road bike. That doesn't help. Of course you have to be flexible enough to get lower on the bike. Never under-estimate how much gain you can get by not sitting up and acting like an air-brake.


Yes i worked very hard on my core strength and flexibility to do so. Shortened forward saddle to open up the hip angle also.
Some of that transferred to the roadie but I could never achieve the relaxed but well braced position that the tt bike gave. The ability to plonk the forearms on the aerobar pads and rest the upper body comfortably shouldnt be underestimated as a contributing factor too imo.
Anyway tt racing is the best. Much more enjoyable than towing around wheel suckers.

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Re: 2 road cyclist vs 1 TT cyclist

Postby scotto » Thu Sep 22, 2016 9:43 am

Calvin27 wrote:2 riders easily.

If you've ever ridden track you know how much ground you can cover even taking turns at half or whole laps.

Even on a short TT, single guy has no chance.


not so sure. my average speed in our club TT over 25km is 1km/h higher than in a bunch race of the same grade.( -> handicap race - so no dawdling). A 4k TT on the track or would be different. I think as the distance increases, the TT gets further aheah

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Re: 2 road cyclist vs 1 TT cyclist

Postby Calvin27 » Thu Sep 22, 2016 11:05 am

scotto wrote:not so sure. my average speed in our club TT over 25km is 1km/h higher than in a bunch race of the same grade.


I think the difference is that a TT you are riding on the line. In a bunch race, you are holding otu a bit for the possibility of a sprint at the end. If you had two 'you's' and they were working together (not racing each other) I rekon they would easily do it faster than one you on a TT.
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Re: 2 road cyclist vs 1 TT cyclist

Postby warthog1 » Thu Sep 22, 2016 2:32 pm

scotto wrote:
not so sure. my average speed in our club TT over 25km is 1km/h higher than in a bunch race of the same grade.( -> handicap race - so no dawdling). A 4k TT on the track or would be different. I think as the distance increases, the TT gets further aheah



ditto.
Handicap racing also. The tt times over the same courses were faster against the scratch bunch trying to chase down limit.

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Re: 2 road cyclist vs 1 TT cyclist

Postby warthog1 » Thu Sep 22, 2016 2:55 pm

Another way of looking at this question is;
Take 3 of the best tters in the world, Tony Martin, Rohan Denis, Fabian Cancellara, it doesn't really matter for the sake of the discussion.
They are all pretty handy on a roadie too, they spend more time on one despite being damn good on a tt machine.
Get a flat 40 km course and put 2 on their roadies. Put the other one on his tt rig all decked out and see who wins. Do the same experiment 3 times so each has a crack at their tt rig.
Does anyone think the result is in question, or even close? ;)

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Re: 2 road cyclist vs 1 TT cyclist

Postby silentC » Thu Sep 22, 2016 3:06 pm

I reckon Nashie's post is convincing for me. The time difference is 20 seconds over 4km between one man TT and a 4-man team. That's 4 people working together in an environment perfect for TT and they are only 8% faster. It's hard to imagine that if you took away two riders and the TT bikes that they would be able to maintain that.

On a course with climbs and corners it would be a different story, but I don't think that is the question being asked.
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Re: 2 road cyclist vs 1 TT cyclist

Postby mikedufty » Thu Sep 22, 2016 3:25 pm

Reminds me of an argument in the Albany Cycle club when someone was dominating the weekly time trials with his Tandem. Some people said they could beat the tandem if allowed to ride in a pair drafting. They ended up trying it and found they were wrong.

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Re: 2 road cyclist vs 1 TT cyclist

Postby Jash Rider » Thu Sep 22, 2016 3:42 pm

My Sunday morning rides are with some guys from Redcliffe tri club. On the hills and short flats I can keep up no problems. Once they hunker down on their tri bars, they pull away like I'm an invalid. I struggle to keep up and have to go to the drops if I don't want to be left behind, pedaling my little legs like porky pig.

This is going from say 34-37kph to 41-43kph (or faster if it's a real smooth bit of tarmac).

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Re: 2 road cyclist vs 1 TT cyclist

Postby Alex Simmons/RST » Fri Sep 23, 2016 10:03 am

mikedufty wrote:Reminds me of an argument in the Albany Cycle club when someone was dominating the weekly time trials with his Tandem. Some people said they could beat the tandem if allowed to ride in a pair drafting. They ended up trying it and found they were wrong.

I've had the pleasure of racing as a solo rider with a tandem in national paracycling road race champs. Attempting to swap off turns with them on the flat was, well, murder. To be expected since the tandem has double the horse power and but hardly any difference in aerodynamics. On the climbs we were well matched, I was perhaps a touch better.

Difference between where W/m^2 matters and where W/kg matters.

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Re: 2 road cyclist vs 1 TT cyclist

Postby Alex Simmons/RST » Fri Sep 23, 2016 10:08 am

Jash Rider wrote:My Sunday morning rides are with some guys from Redcliffe tri club. On the hills and short flats I can keep up no problems. Once they hunker down on their tri bars, they pull away like I'm an invalid. I struggle to keep up and have to go to the drops if I don't want to be left behind, pedaling my little legs like porky pig.

This is going from say 34-37kph to 41-43kph (or faster if it's a real smooth bit of tarmac).

For no change in aerodynamics, on flat terrain when solo:
Going from sustaining 37km/h to 43km/h requires ~50% increase in power output.
Going from sustaining 34km/h to 43km/h requires ~90% increase in power output.

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Re: 2 road cyclist vs 1 TT cyclist

Postby Jash Rider » Sat Sep 24, 2016 9:02 am

Alex Simmons/RST wrote:
Jash Rider wrote:My Sunday morning rides are with some guys from Redcliffe tri club. On the hills and short flats I can keep up no problems. Once they hunker down on their tri bars, they pull away like I'm an invalid. I struggle to keep up and have to go to the drops if I don't want to be left behind, pedaling my little legs like porky pig.

This is going from say 34-37kph to 41-43kph (or faster if it's a real smooth bit of tarmac).

For no change in aerodynamics, on flat terrain when solo:
Going from sustaining 37km/h to 43km/h requires ~50% increase in power output.
Going from sustaining 34km/h to 43km/h requires ~90% increase in power output.



What's the difference when going from the brifters to the tri bars, in a group? I know that when they're on their tri bars they can cruise along at 41-43kph for as long as they want if it's flat. Fortunately for me those flat sections aren't 20km long.

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Re: 2 road cyclist vs 1 TT cyclist

Postby ironhanglider » Sat Sep 24, 2016 9:34 am

When people start using aero-bars in a group, I get out of that group. I have no interest being caught up in someone else's crash.

On public roads in open conditions there are too many variables. Even on an indoor velodrome things go wrong very easily.

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Re: 2 road cyclist vs 1 TT cyclist

Postby DaveQB » Mon Sep 26, 2016 8:44 pm

Alex Simmons/RST wrote:For example, a 5% improvement in speed from road to TT bike at threshold power is not all that wild (certainly for me it's not), and for the pair on the road bikes that requires the rider in front to be putting out ~15% more power than the TT rider.



Excellent post Alex Simmons/RST.
Thank you for that. My question is why 15% more power if the TT guy has a 5% speed increase? It's not 5% more power?

It's been a great thread to read. I am glad I posed the question 8)
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Re: 2 road cyclist vs 1 TT cyclist

Postby warthog1 » Mon Sep 26, 2016 9:00 pm

Wind resistance increases exponentially with speed ie j curve on a graph with speed on the horizontal axis and drag on the vertical axis.

Image
Last edited by warthog1 on Mon Sep 26, 2016 9:03 pm, edited 1 time in total.

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Re: 2 road cyclist vs 1 TT cyclist

Postby MattyK » Mon Sep 26, 2016 9:02 pm

DaveQB wrote:
Alex Simmons/RST wrote:For example, a 5% improvement in speed from road to TT bike at threshold power is not all that wild (certainly for me it's not), and for the pair on the road bikes that requires the rider in front to be putting out ~15% more power than the TT rider.



Excellent post Alex Simmons/RST.
Thank you for that. My question is why 15% more power if the TT guy has a 5% speed increase? It's not 5% more power?

It's been a great thread to read. I am glad I posed the question 8)

Drag goes up as the square of speed. Power goes up as the cube of speed. 5% faster = 1.05 x 1.05 x 1.05 = 1.157, or 15.7% more power

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Re: 2 road cyclist vs 1 TT cyclist

Postby Alex Simmons/RST » Tue Sep 27, 2016 8:05 am

MattyK wrote:
DaveQB wrote:
Alex Simmons/RST wrote:For example, a 5% improvement in speed from road to TT bike at threshold power is not all that wild (certainly for me it's not), and for the pair on the road bikes that requires the rider in front to be putting out ~15% more power than the TT rider.



Excellent post Alex Simmons/RST.
Thank you for that. My question is why 15% more power if the TT guy has a 5% speed increase? It's not 5% more power?

It's been a great thread to read. I am glad I posed the question 8)

Drag goes up as the square of speed. Power goes up as the cube of speed. 5% faster = 1.05 x 1.05 x 1.05 = 1.157, or 15.7% more power


Yes, the very well established mathematical relationship between speed and power is a cubic equation although it has both cubic (air resistance) and linear components (gravitational and rolling resistance). There are also other minor frictional components that end up being quasi linear. And of course there is an energy demand to accelerate which depends on the rate of change in kinetic energy (and like gravitational potential, kinetic energy can decrease as well). This is the equation including the acceleration component, which has been verified many times since:

Image

It looks worse than it is, and the smaller components such as wheel bearing resistance, wheel rotational factors etc can be reasonably combined into the main elements to simplify it without too much error, then we get:

P = Pat + Prr + Ppe + Pke
where
P = total power
Pat = power to over come air resistance
Prr = power to to overcome rolling resistance (tyres, road surface)
Ppe = power to to change gravitational potential (i.e. up / down hills)
Pke = power required to accelerate (i.e. to change speed)

Looking at each:

Pat= 1/2 * ρ * Va^2 * Vg * CdA
where:
ρ = air density
Va = relative air speed
Vg = bike's ground speed
CdA = coefficient of drag * effective frontal area

Prr = Vg * m * g * Crr * cos(arctan(G))
where:
m = total mass of bike + rider
g = acceleration due to gravity
Crr = coefficient of rolling resistance
G = road gradient (can be negative)

Ppe = Vg * m * g * sin(arctan(G))

Pke = 1/2 * m * (Vf^2 - Vi^2)/(Tf - Ti)
where:
Vf = final velocity
Vi = initial velocity
Tf = final time
Ti = initial time

Add those together and you get total power at the rear wheel:

P = [1/2 * ρ * Va^2 * Vg * CdA] + [Vg * m * g * Crr * cos(arctan(G))] + [Vg * m * g * sin(arctan(G))] + [1/2 * m * (Vf^2 - Vi^2)/(Tf - Ti)]

To calculate power at the cranks it requires multiplying P by a drivetrain efficiency factor, which is typically ~ 0.97 - 0.98.

Provided you use SI units throughout, then power will be in the unit of watts.

So on flat road, Ppe drops to zero (since gradient is zero) and if riding steady state velocity, Pke is also zero (since no change in velocity), meaning we are left with power to overcome air resistance and rolling resistance.

If you look at the formula for rolling resistance, it's very similar to the one for changes in gravitational potential. Hence rolling resistance is equivalent to adding ~0.5% to whatever gradient you happen to be riding. The Crr varies depending on the riding surface, quality of tyres and air pressure in the tyres as well. Typical Crr values are in the 0.0025 range for a good wooden velodrome to 0.005 for typical roads and race tyres (smooth asphalt and good tyres perhaps 0.004) and much higher for rough terrain and larger more knobbly tyres.

On flatter terrain the air resistance dominates the total energy demand, and we can see that it is a cubic equation, hence the rapid increase in power required for a change in speed.

However on steep climbs the gravitational potential energy part of the equation dominates the energy demand, and that is linear relationship hence the change in speed is nearly the same as the change in power required.

Here is an example of how the proportion of energy demand factors changes with change in gradient for steady state cycling:

Image

As you can see, it's clear that the ratio of power to aerodynamic drag is what matters most on flatter terrain, and the ratio of power to mass is what matters most when climbing steep terrain.


Now the equation above is relatively easy to solve power from a given constant speed, provided you have all the inputs (wind velocity, air density, CdA, mass, Crr and gradient). Of course some of those values are not so easy to arrive at, in particular CdA, Crr and wind velocity. There are methods to test for such things. CdA for instance is high variable by individual and also depending on the individual's set up, clothing, equipment, position etc. Dynamically measuring wind velocity in the field is quite a difficult thing to do accurately. Power estimates are highly sensitive to small changes in wind velocity assumptions.

If you add in accelerations it becomes a bit more complex because it's now a dynamically changing scenario requiring a method suitable for such scenarios (i.e. calculus). It's doable in a spreadsheet with a method called forward integration.

Solving speed from a given power though is somewhat harder as solving cubic equations is rather tricky and there is not always a closed form solution (especially the case on steepish negative gradients). Cardano's closed form method works for most scenarios, else you need to solve using Newton's method or something similar. I did the algebra required to flip (the more complex version of) the equations and use both Cardano's and Newton's methods to solve as needed.

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Re: 2 road cyclist vs 1 TT cyclist

Postby g-boaf » Tue Sep 27, 2016 8:13 am

DaveQB wrote:
Alex Simmons/RST wrote:For example, a 5% improvement in speed from road to TT bike at threshold power is not all that wild (certainly for me it's not), and for the pair on the road bikes that requires the rider in front to be putting out ~15% more power than the TT rider.



Excellent post Alex Simmons/RST.
Thank you for that. My question is why 15% more power if the TT guy has a 5% speed increase? It's not 5% more power?

It's been a great thread to read. I am glad I posed the question 8)


Aero is pretty important for top speed. Remember in the old days of F1 with the Stewart-Ford F1 car. It didn't have the most powerful engine, but it was clocking the highest straight line speeds (357km/h) at Hockenheimring. How? It was very aerodynamic. It's the same with bikes on a flat course. When hills are involved, it comes down to weight versus power.

For the technical bit, I think the post above covers everything in massive detail.

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Re: 2 road cyclist vs 1 TT cyclist

Postby warthog1 » Tue Sep 27, 2016 12:38 pm

Alex Simmons/RST wrote:
MattyK wrote:
DaveQB wrote:

Excellent post Alex Simmons/RST.
Thank you for that. My question is why 15% more power if the TT guy has a 5% speed increase? It's not 5% more power?

It's been a great thread to read. I am glad I posed the question 8)

Drag goes up as the square of speed. Power goes up as the cube of speed. 5% faster = 1.05 x 1.05 x 1.05 = 1.157, or 15.7% more power


Yes, the very well established mathematical relationship between speed and power is a cubic equation although it has both cubic (air resistance) and linear components (gravitational and rolling resistance). There are also other minor frictional components that end up being quasi linear. And of course there is an energy demand to accelerate which depends on the rate of change in kinetic energy (and like gravitational potential, kinetic energy can decrease as well). This is the equation including the acceleration component, which has been verified many times since:

Image

It looks worse than it is, and the smaller components such as wheel bearing resistance, wheel rotational factors etc can be reasonably combined into the main elements to simplify it without too much error, then we get:

P = Pat + Prr + Ppe + Pke
where
P = total power
Pat = power to over come air resistance
Prr = power to to overcome rolling resistance (tyres, road surface)
Ppe = power to to change gravitational potential (i.e. up / down hills)
Pke = power required to accelerate (i.e. to change speed)

Looking at each:

Pat= 1/2 * ρ * Va^2 * Vg * CdA
where:
ρ = air density
Va = relative air speed
Vg = bike's ground speed
CdA = coefficient of drag * effective frontal area

Prr = Vg * m * g * Crr * cos(arctan(G))
where:
m = total mass of bike + rider
g = acceleration due to gravity
Crr = coefficient of rolling resistance
G = road gradient (can be negative)

Ppe = Vg * m * g * sin(arctan(G))

Pke = 1/2 * m * (Vf^2 - Vi^2)/(Tf - Ti)
where:
Vf = final velocity
Vi = initial velocity
Tf = final time
Ti = initial time

Add those together and you get total power at the rear wheel:

P = [1/2 * ρ * Va^2 * Vg * CdA] + [Vg * m * g * Crr * cos(arctan(G))] + [Vg * m * g * sin(arctan(G))] + [1/2 * m * (Vf^2 - Vi^2)/(Tf - Ti)]

To calculate power at the cranks it requires multiplying P by a drivetrain efficiency factor, which is typically ~ 0.97 - 0.98.

Provided you use SI units throughout, then power will be in the unit of watts.

So on flat road, Ppe drops to zero (since gradient is zero) and if riding steady state velocity, Pke is also zero (since no change in velocity), meaning we are left with power to overcome air resistance and rolling resistance.

If you look at the formula for rolling resistance, it's very similar to the one for changes in gravitational potential. Hence rolling resistance is equivalent to adding ~0.5% to whatever gradient you happen to be riding. The Crr varies depending on the riding surface, quality of tyres and air pressure in the tyres as well. Typical Crr values are in the 0.0025 range for a good wooden velodrome to 0.005 for typical roads and race tyres (smooth asphalt and good tyres perhaps 0.004) and much higher for rough terrain and larger more knobbly tyres.

On flatter terrain the air resistance dominates the total energy demand, and we can see that it is a cubic equation, hence the rapid increase in power required for a change in speed.

However on steep climbs the gravitational potential energy part of the equation dominates the energy demand, and that is linear relationship hence the change in speed is nearly the same as the change in power required.

Here is an example of how the proportion of energy demand factors changes with change in gradient for steady state cycling:

Image

As you can see, it's clear that the ratio of power to aerodynamic drag is what matters most on flatter terrain, and the ratio of power to mass is what matters most when climbing steep terrain.


Now the equation above is relatively easy to solve power from a given constant speed, provided you have all the inputs (wind velocity, air density, CdA, mass, Crr and gradient). Of course some of those values are not so easy to arrive at, in particular CdA, Crr and wind velocity. There are methods to test for such things. CdA for instance is high variable by individual and also depending on the individual's set up, clothing, equipment, position etc. Dynamically measuring wind velocity in the field is quite a difficult thing to do accurately. Power estimates are highly sensitive to small changes in wind velocity assumptions.

If you add in accelerations it becomes a bit more complex because it's now a dynamically changing scenario requiring a method suitable for such scenarios (i.e. calculus). It's doable in a spreadsheet with a method called forward integration.

Solving speed from a given power though is somewhat harder as solving cubic equations is rather tricky and there is not always a closed form solution (especially the case on steepish negative gradients). Cardano's closed form method works for most scenarios, else you need to solve using Newton's method or something similar. I did the algebra required to flip (the more complex version of) the equations and use both Cardano's and Newton's methods to solve as needed.



Well, you did ask for an explanation Dave :shock:

I believe you got it 8)

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Re: 2 road cyclist vs 1 TT cyclist

Postby mikesbytes » Tue Sep 27, 2016 3:54 pm

Alex has covered the technical

One aspect that has caused variation in the answers is that the same rider performs differently in TT vs road
- The difference in aero between TT and road bikes will vary between bikes
- The ability to punch out a constant power (TT) vs the abilty to output power in a farlek delivery (2*road swapping turns)

If it was 3 of me, the difference in aero between my TT and road setup isn't huge, I can hold my body in any position for an extended duration, I have the flexibility and strength. Power output wise, I feel I am good at farlek, it comes from the nature of my work.

For someone else the answer is completely different
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Re: 2 road cyclist vs 1 TT cyclist

Postby DaveQB » Tue Sep 27, 2016 8:09 pm

Alex Simmons/RST wrote:
Yes, the very well established mathematical relationship between speed and power is a cubic equation although it has both cubic (air resistance) and linear ....



WOW!!
I need some time to read this a few times but I get the gist of it. Thank you.

warthog1 wrote:
Well, you did ask for an explanation Dave :shock:

I believe you got it 8)


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Re: 2 road cyclist vs 1 TT cyclist

Postby Duck! » Tue Sep 27, 2016 9:43 pm

The really simplified gist of Alex's post is that the faster you go, the "thicker" the air around you becomes, so requires big chunks more power to get similar or even smaller increases in speed.

Two riders will generally be faster than a solo on the same equipment, because the presence of the second rider, if close enough behind, can alter the airflow behind the lead rider, and reduce drag, allowing the leader to also ride faster than they otherwise would. Whether it's enough to counter the improved aero setup of a single TT rider would need to be tested.
I had a thought, but it got run over as it crossed my mind.

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Re: 2 road cyclist vs 1 TT cyclist

Postby rodneycc » Tue Sep 27, 2016 10:26 pm

So the longer the ride goes does the two road riders have the advantage or the TT rider has the advantage? I would of thought the two road riders would of had the advantage the longer it went?
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