How (much exactly) does power:weight ratio convert into speed?

[Slowbee]

as a side bar ... (not on a riser bar), how much does it matter if the rider looses a 1kg or the bike gets 1kg lighter ?

[Capricorn]

a few snippets of interest.

Wikipedia first:

Note that the power required to overcome friction and gravity is proportional only to rider weight and ground speed. The aerodynamic drag is roughly proportional to the square of the relative velocity of the air and the bike. Being that the total power requirement to propel the bike forward is a sum of these two variables multiplied by speed, the degree of proportionality between power requirement and speed varies according to their relative magnitude, in an interval between the linear and cube: at higher speeds (riding fast on a flat road) power required will be close to being a cube function of speed, at lower speeds (climbing a steep hill) it will be close to being a linear function of speed.

The human body runs at about 24% efficiency for a relatively fit athlete, so for every kilojoule delivered to the pedals the body consumes 1 kcal (4.2 kJ) of food energy.^{[citation needed]}

Obviously, both of the lumped constants in this equation depend on many variables, including drive train efficiency, the rider's position and drag area, aerodynamic equipment, tire pressure, and road surface. Also, recognize that air speed is not constant in speed or direction or easily measured. It is certainly reasonable that the aerodynamic lumped constant would be different in cross winds or tail winds than in direct head winds, as the profile the bike/rider presents to the wind is different in each situation. Also, wind speed as seen by the bike/rider is not uniform except in zero wind conditions. Weather report wind speed is measured at some distance above the ground in free air with no obstructing trees or buildings nearby. Yet, by definition, the wind speed is always zero right at the road surface. Assuming a single wind velocity and a single lumped drag constant are just two of the simplifying assumptions of this equation. Computational fluid dynamicists have looked at this bicycle modeling problem and found it hard to model well. In layman's terms, this means that much more sophisticated models can be developed, but they will still have simplifying assumptions.

Given this simplified equation, however, one can calculate some values of interest. For example, assuming no wind, one gets the following results for kilocalories required and power delivered to the pedals (watts):

• 175 W for a 90 kg bike + rider to go 9 m/s (20 mph or 32 km/h) on the flat (76% of effort to overcome aerodynamic drag), or 2.6 m/s (5.8 mph or 9.4 km/h) on a 7% grade (2.1% of effort to overcome aerodynamic drag).
  

• 300 W for a 90 kg bike + rider at 11 m/s (25 mph or 40 km/h) on the flat (83% of effort to overcome aerodynamic drag) or 4.3 m/s (9.5 mph or 15 km/h) on a 7% grade (4.2% of effort to overcome aerodynamic drag).
  

• 165 W for a 65 kg bike + rider to go 9 m/s (20 mph or 32 km/h) on the flat (82% of effort to overcome aerodynamic drag), or 3.3 m/s (7.4 mph or 12 km/h) on a 7% grade (3.7% of effort to overcome aerodynamic drag).
  

• 285 W for a 65 kg bike + rider at 11 m/s (25 mph or 40 km/h) on the flat (87% of effort to overcome aerodynamic drag) or 5.3 m/s (12 mph or 19 km/h) on a 7% grade (6.1% of effort to overcome aerodynamic drag).
  

Shaving 1 kg off the weight of the bike/rider would increase speed by 0.01 m/s at 9 m/s on the flat (5 seconds in a 20 mph (32 km/h), 25-mile (40 km) TT). Losing 1 kg on a 7% grade would be worth 0.04 m/s (90 kg bike + rider) to 0.07 m/s (65 kg bike + rider). If one climbed for 1 hour, saving 1 lb would gain between 225 and 350 feet (107 m) – less effect for the heavier bike + rider combination (e.g., 0.04 mph (0.06 km/h) * 1 h * 5,280 ft (1,609 m)/mi = 225 ft).

[Capricorn]

then these two, which don't so much as go into detail about the relative performance deltas between rider+bike mass values, but rather some coaching insight into maximizing YOUR performance, which is the actual objective IMO:

 

from wattbike:

 

What is power to weight ratio [P/Kg]?

Power to weight [P/Kg] ratio is the relationship between:

• Power (measured is watts [W])
  
• Weight (measured in kilograms [kg])
  

For example if a cyclist produces a maximum minute power of 350 W during a cycling ramp test and weighs 70 Kgs the power to weight ratio [P/Kg] is expressed as: P/Kg = 350/70 = 5 Watts per kilogram of body weight. A cyclist weighing 90 Kgs achieving the same maximum minute power would have a power to weight ratio [P/Kg] ofP/Kg = 350/90 = 3.89 Watts per kilogram of body weight.

Wattbike Expert Software (version 2.50.42 upwards) automatically calculates the Power to Weight ratio [P/kg] providing the correct weight, in kilograms has been entered in the cyclist’s personal file.

Why measure power to weight ratio [P/Kg]

The purpose of measurement is to optimise power to weight ratio relative to a specific task, for example cycling up a hill or during a sprint of short duration (note also the consideration of drag and rolling road resistance where surface area and weight are equally relevant even on a flat road course).

Optimisation can be done in two ways which can be combined:

• Increasing absolute power
  
• Decreasing weight
  

Losing weight as a means of improving the ratio is not recommended unless clearly overweight. Dieting to attain an “ideal” cycling weight can be very counter productive. It’s not as simple as losing weight, if lean muscle mass is lost absolute power output will be reduced as the means for producing the power has gone.

The best option is to focus on optimising power whilst balancing diet and weight. It is far simpler to maximise power than control body weight. Weight loss can usually be achieved naturally by a structured training and racing program. By focusing on training to maximise power (increasing lean muscle mass) power and weight ratio can be optimised.

The basic science of power to weight ratio[P/Kg]

The best explanation is to consider hill cycling ability. Assume two cyclists of equal ability and identical equipment riding uphill side-by-side. The first cyclist weighs 85 Kgs and has an average power on the climb of 450 watts. The second cyclist weighs 65 Kgs and has an average power on the climb of 380 watts.

Looking at pure absolute power the natural assumption is that the first cyclist would easily beat the second cyclist on this climb because of the 70 watt power difference.

However, power is not the only variable that cyclists have to contend with whilst climbing. Part of a cyclist’s climbing power is used to move horizontally in a forward direction and part to overcome the influence of gravity in moving in an uphill direction (i.e. climbing the hill).

When weight is taken into account in addition to absolute climbing power the result for each cyclist is:

• Cyclist 1 P/Kg= 5.29 W/Kg (450/85)
  
• Cyclist 2 P/Kg = 5.85 (380/65)
  

Cyclist 2 in most circumstances would get to the top of the hill first even though cyclist 1 is producing 18% more absolute power than cyclist 2.

What is a typical power to weight ratio

It really depends on the type of cyclist. Sprinters typically have high short duration power output and lower endurance scores whilst endurance cyclists may have low short duration power and high endurance scores. Weight (lean muscle mass) is an advantage for short duration sprint cyclists.

As an example, world class male sprint cyclists typically weigh over 80 Kgs and in some cases over 90 Kgs and are capable of peak power scores in the range 1750-2250 W and max minute power of 360-400W. Conversely world class male endurance cyclists typically weigh closer to 70-75 Kgs and whilst producing lower peak power scores of 1000-1250W have a much higher max minute power score of 420-500W.

World class female sprint cyclists typically weigh 60-65 Kgs with peak power scores of 1000-1500W, world class female endurance cyclist typically weigh well below 60 Kgs with max minute power score of 320-350W

On a Wattbike we have seen scores within these ranges - the highest peak power score, so far is 2300W (male) and 1600W (female). Testing peak power and maximum minute power on a Wattbike is an easy process. A 6 second Peak Power Test is built into the Wattbike Performance Computer and Maximum Minute Power Ramp Test protocols are easy to construct on a Wattbike and analyse using Wattbike Expert Software.

How to improve power to weight ratio [P/Kg]

In the example above cyclist 1 would need to lose 9 Kgs to increase power to weight ratio to equal that of cyclist 2. A rapid reduction in body weight of this magnitude would result in the loss of lean muscle mass responsible for producing the power in the first place. The better choice would be to focus on increasing absolute power using a structured training program.

The advantage of the Wattbike is the control and immediate, accurate feedback on relevant parameters such as gearing (resistance), cadence (see section on Gearing and Cadence), power output, technique (using the unique Polar View facility of the Wattbike Performance Computer and Expert Software) and many other cycling parameters to optimize performance.

[Capricorn]

and something from a coach:

Application of POWER-TO-WEIGHT Ratio to Cycling Performance

 

by Mark Consugar

It is safe to say that one of the major buzzwords in cycling today is POWER. It has become common to gauge an athlete’s potential not so much by their maximum or average sustainable speeds, their maximum or average heart rates, their equipment or their appearance (don’t tell me you’ve never sized someone up by checking out their legs before a ride/race), but by their POWER OUTPUT at or during a given effort. There is no better testament of this than the availability and demand of affordable power meters on the market today. These training devices, available only to elite athletes a few years ago (i.e. SRM Cranks), are now becoming as or MORE common with amateur cyclists than heart rate monitors. One of the more common modes of utilizing an athlete’s power data is in determining their POWER-TO-WEIGHT ratio (P/W) during given efforts, particularly climbing.

In this article I would like to discuss P/W and how it can be used to optimize performance. I will also highlight a practical example of how P/W is used in assessing and improving a rider’s climbing performance and why. Finally, I will outline a few training methods a cyclist could use to improve their P/W.

What is the Power-To-Weight Ratio (P/W)?

Power-To-Weight (P/W) is nothing more than a fraction based on two variables: POWER (measured is watts) and WEIGHT (measured in kilograms or pounds). The purpose in determining and tracking one’s P/W is to MAXIMIZE its value relative to a specific task (i.e. climbing). This can be done in one (or a combination) of two ways: 1) INCREASE power (numerator), or 2) DECREASE weight (denominator).

As an athlete and coach, I have experience in manipulating this ratio according to BOTH variables in order to track performance improvements. Where I have been the MOST surprised is in the poor execution of this equation. For example, if I was to ask a group of cyclists how they could improve their P/W, I would wager that upwards of 80% of them would say by losing weight. Although this is a 100% correct answer, in most cases it is an ill advised one. Cyclists in general are some of the most weight (image)-conscious athletes I know, second only to wrestlers (and not of the WWE variety). We watch our “idols” riding the Tour de France and think that to be able to excel at our sport like they do we have to “look” like they do: shallow face, thin upper-body, massive legs. When dealing with my athletes I like to remind them that: 1) professional cyclists are paid to bicycle around France (or where ever) to win races- that is their job!, and 2) their diets are monitored by AT LEAST one (usually more) professional dieticians such that the rider’s health is never brought into question but is optimized to yield MAXIMUM power output with the LEAST amount of “unnecessary” weight gain.

For us, the “weekend warriors” and/or recreational cyclists, we ride for health and enjoyment; our careers are aligned along other paths. What I, and MANY far more experienced coaches, scientists and physiologists than I, have found is that “starving” ourselves to attain/maintain our “ideal” cycling weight can be very counter productive. The truth is that although we might lose weight, identifying WHERE the weight loss occurred is the real question. Put simply, if you are losing LEAN MUSCLE MASS, you are indirectly lowering your power output by catabolizing the means for generating your POWER.

As a result, I try to get my athletes to focus on optimizing the numerator, or POWER, and let the denominator (WEIGHT) take care of itself. Truth be told, athletes and coaches have FAR MORE control over maximizing their absolute power than they do minimizing their body weight. Ironically, most cyclists find that their weight loss goals are usually attained naturally while riding/racing/training during a season. By focusing our energies through training to maximize POWER, which increases lean muscle mass and can decreases overall body weight safely and naturally, BOTH P/W variables are optimized to meet the athlete’s needs.

Application of P/W:

Utilization of a rider’s P/W is mot commonly found when assessing their climbing ability. Let us assume there are two riders of equivalent abilities with identical bikes and components. Both cyclists will be climbing the same climb side-by-side at exactly the same time on exactly the same day under exactly the same conditions.

Rider-1 weighs in at 175 lbs. and has an average sustainable power on said climb of 475 watts. Rider-2 weighs in at 130 lbs. and has an average sustainable power on the same climb of 380 watts. If someone were to base their opinion of each rider’s climbing ability solely on their power, they might think that Rider-1 would be able to easily beat Rider-2 to the top of the mountain. Granted, Rider-1’s sustainable climbing power is 95 watts GREATER THAN Rider-2’s (ca. 20%); however, power is not the only variable riders are aware of while dragging themselves up a climb. TOTAL Weight (body, bike frame, components, wheels, etc.) also plays an important role.

 

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The effort a climbing rider (measured in power) is directed in part along each of these two vectors. Although the rider’s mass factors into each of these directional vectors, it plays a bigger role as WEIGHT when you factor in the affect of gravity along the vertical vector. Stated simply, P/W could also represent H/V as a means of determining how much of a rider’s climbing power will be used to move along the horizontal vector (general direction of progression) compared to overcoming the influences of gravity along the vertical vector.

Getting back to our two riders. When we now account for each of their weights in addition to their climbing powers, we find that P/W₁ = 2.71 watts/lb., whereasP/W₂ = 2.92. All things being equal, Rider-2 will get to the top of the climb before Rider-1, even though Rider-1 can generate approximately 20% more power than Rider-2.

Improving One’s P/W:

As a coach, I would be hard pressed to get Rider-1 to shed the 12+ lbs. needed to increase his P/W equal to or above that of Rider-2, especially when you consider BOTH riders are probably at or near top physical condition already. Any wholesale reduction in Rider-1’s body weight (and we’re talking an ca. 7% weight loss) could result in the simultaneous loss of lean muscle mass, which is responsible for generating the power. The better choice would be to focus on increasing Rider-1’s power by 35+ watts using a structured training program that would be far less invasive (physically and psychologically) and far more sustainable.

Below are a couple workouts that could be implemented into a rider’s yearly training plan to help improve their “potential” power output. With improved power would come improved climbing, sprinting and time trialing:

1- Hit the gym!

An athlete’s secret weapon to in-season success is performing resistance workouts in the gym during the off- and early-season periods. Performing resistance workouts that focus on the legs (squats, lunges, curls, extensions) as well as the core (abs, lower back, external obliques) will all assist in building the lean muscle mass essential to generating raw power. Cyclists seem to be afraid of “gaining weight” in the gym, choosing to overly focus on the P/W denominator. But trust me, the extra 15 lbs. of lean muscle mass you might gain in order to generate an additional 50 – 125 watts will be well worth it!

2- Muscle Tension Intervals

These “on-the-bike” HIGH RESISTANCE/TENSION intervals are usually done on an indoor trainer or gradual climb. You will climb over-geared such that your average cadence is between 50 – 60 rpm, staying seated and focusing on a smooth circular pedal stroke throughout the effort. Intervals should last between 5 – 10 minutes, with recovery between efforts being half the interval time (i.e. 8 min. HOT, 4 min. REST). These intervals help translate the raw power gains from the gym to the bike, and are synonymous to doing squats/lunges during a ride.

3- Climbing Repeats

These are the coup-de-grace for riders looking to improve their climbing AND time trialing performances. These intervals are best performed on long gradual climbs (i.e. Millville, Country Club Road, State RR Course in Plainview, etc.) at cadences between 75 – 85 rpm. Stay seated while climbing and focus on a smooth circular pedal stroke. Intervals should last the extent of the climb, with recovery between efforts equivalent to that of the interval. Your Heart Rate should read between 85 – 90% of your maximum.

[Hairy]

Take a back pack and fill it with bricks or some other heavy items.

 

Go ride on a flat Road and then a climb.

 

Take Off back pack and repeat. ....You will then have the answer to your question

[Robrider]

as a side bar ... (not on a riser bar), how much does it matter if the rider looses a 1kg or the bike gets 1kg lighter ?

 

If they are putting out the same power it is the same.

 

But if you are talking about a person doing training to lose that 1kg, they will probably have increase aerobic/power benefits.

[Robrider]

MTB related.

 

Not a complicated question, but I don't think an obvious answer.

 

If one obtains a power:weight ratio improvement of 10% - what % speed improvement would this render?

 

1. On the one side I'm thinking that power:weight does not consider wind resistance...so a 10% P:W would be - say 7 % speed improvement.

2. On the other side a better P:W ratio means that the legs have less stress, and should thus last longer...and over a proper distance render a better time. Maybe even better than 10%.

 

Does anyone have some facts/real experiences to share?

And if you just feel like giving an subjective view - then OK, but please just let us know that you are philosophy-ing.

 

I never really understand why people want specific answers to questions like these. You can make a lot of observations (like up hills power to weight means more than on a flat), but at the end of the day, there are so many variables and the equations are non-linear, so you can't just equate a specific percentage that fits all situations.

 

When I say non-linear, here is an example: if you are riding 10km/h and double your wattage, say you are at 20km/h. But you will have to increase your wattage by a lot more to get from 30km/h to 40km/h. So you can't say that if you increase your power by 10% then your speed will increase by 10%... similarly your question doesn't make sense.

 

At the end of the day, you know power to weight helps improve. You also know it is more important uphills, where gravity is dominant. It is less important when aerodynamics is dominant, such as flats and in headwinds.

 

What are you going to do with the specific answer if you get it? (not possible)

Edited March 29, 2014 by Robrider

[Chopper Jr]

Numbers don't mean a thing!

 

Worry about the gap between yourself and the oke in front of you. Train harder until you're the oke in front.

 

Simple!

[evolve]

Being leaner and having a light bike makes you look fast and feel fast.........ride as best you can eat were you are are comfy and ride a bike that you like......as long you feel good it's ok.

Too much factual overload - as above will just make trouble, and bring out the popcorn

[Dustbug]

A simple answer based on actual races 2012 and 2013 Hill2Hill my experience training distances etc very similar but 2013 2x cadence power training courses

2012 body weight 94 kgs distance 98.6kms avg speed 12.3kms per hour finishing time 08h03

2013 body weight 89 kgs distance 95.7 kms avg speed 17.3kms per hour finishing time 06h07

power increase over the 2 cadence power training courses 12% in 2013

same bike ridden with same kit in both races

 

answer power to weight ratio does matter