Yet Another Cycling Forum
General Category => The Knowledge => Further and Faster => Topic started by: Numpty on 11 March, 2019, 08:08:09 am
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Anybody here any good at sums? Recently I have ridden quite a lot in high winds, and I would love to know how this is affecting my performance, bearing in mind I usually end up exhausted, but the more I delve into it the more I submerge myself in Fluid Dynamics, which is alien to me. Please does anyone have a formula to calculate (perhaps approximately) if I am facing a headwind of 15mph (say), and I want to ride effectively at 15mph(say), what is the speed I need to actually ride? It cannot simply be a subtraction, because if I am riding at 10mph into a 15mph headwind I do not go backwards. Alternatively if Garmin says I averaged 15mph into a 15mph headwind, what did I really achieve?
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there is a website
http://www.kreuzotter.de/english/espeed.htm (http://www.kreuzotter.de/english/espeed.htm)
Enjoy
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The trivial answer is 15mph but you'll have an apparent air speed of 30mph.
Are you looking for an equivalent power output rather than speed? Or put another way an equivalent "still air speed"?
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I find that if the wind speed exceeds 30mph, my ground speed reduces to around 0mph.
Usually because I haven't bothered going out.
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your garmin gives speed across the ground, and actually only in a horizontal direction. So it lies when you are on anything other than the flat. The degree of lying depends on the slope.
In fluid dynamics terms this is a pretty complex set of euqations (I might have had a stab at it 20 years ago), mostly because you as a human bean is not uniform, and then attach you to a BSO which is more non-uniform and is varying in its non uniformity. You could make several approximations to uniformity, but effectively the question you are asking is how much more drag is being created by me cycling into a wind, assumed headwind, than cycling into still air.
So effectively normal drag = 15mph (say) into still air, effective windspeed 15mph
New drag = 15mph "speed" plus 15mph wind = 30mph "drag"
I believe form drag scales with square of speed, so x 2 speed = x 4 energy output required to overcome that aspect of drag, then you have friction losses (drivetrain plus skinfriction), then you have your biomechanical efficiency, then your biochemical efficiency
I'd say go find a wind tunnel, or a CFD expert.
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there is a website
http://www.kreuzotter.de/english/espeed.htm (http://www.kreuzotter.de/english/espeed.htm)
Enjoy
He doesn't take the road surface into account.
The force exerted by aerodynamic drag varies as the square of the combined rider and wind speeds, which means that the power required to overcome it varies as the cube. When I've incorporated this in programs I've taken the resultant of the two velocities, with the wind speed multiplied by the cos of the angle of incidence, but I'm by no means sure this is valid for drag. I've always had the impression that it's easier to ride straight into the wind than at an angle of < 45° to it, probably because when you're riding straight into it you have a smaller frontage and can get into a better aerodynamic shape.
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Because physics is a git, the arc in which you're impeded (headwind) is greater than the arc in which you're assisted (tailwind). ISTR it's something like 200' headwind, 160' tailwind; so it has to be quite noticeably behind you before you get "help".
The effect of the wind on Saturday was that I was even more of a miserable bugger on our bike than usual.
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You are of course expressing an average speed and since it is not a linear relationship between speed and effort, you cannot just take that and multiple by some number to come up with an average "extra" effort. However, taking the output of one of the online calculators the estimate would be that for every hour you are cycling at 15mph into a 15mph headwind you will burn an extra 170 Calories over what you would burn if the wind was still.
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The effect of the wind on Saturday was that I was even more of a miserable bugger on our bike than usual.
I think my most impressive strop was when the bike blew over for the second time while I was trying to mend my second puncture on a grass verge.
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your garmin gives speed across the ground, and actually only in a horizontal direction. So it lies when you are on anything other than the flat. The degree of lying depends on the slope.
Does this also apply if you use a wheel rotation sensor?
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The effect of the wind on Saturday was that I was even more of a miserable bugger on our bike than usual.
I think my most impressive strop was when the bike blew over for the second time while I was trying to mend my second puncture on a grass verge.
The effect of incessant headwind on a loaded Streetmachine is surprisingly hard to distinguish from that of a rear-wheel puncture. I kept stopping to reassure myself that the tyres really were properly inflated. Unfortunately, they were.
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your garmin gives speed across the ground, and actually only in a horizontal direction. So it lies when you are on anything other than the flat. The degree of lying depends on the slope.
Does this also apply if you use a wheel rotation sensor?
I don't see why it would
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Not if the rear wheel sensor is the sole judge of speed, that would then be with reference to the road surface rather than point to point as by GPS.
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You are of course expressing an average speed and since it is not a linear relationship between speed and effort, you cannot just take that and multiple by some number to come up with an average "extra" effort. However, taking the output of one of the online calculators the estimate would be that for every hour you are cycling at 15mph into a 15mph headwind you will burn an extra 170 Calories over what you would burn if the wind was still.
Cool, you're suggesting an integral approach. I wish I could remember how to do that. ???
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your garmin gives speed across the ground, and actually only in a horizontal direction. So it lies when you are on anything other than the flat. The degree of lying depends on the slope.
The horizontal plane accuracy of GPS is generally 3 times better than the vertical accuracy, and so the smoothing algorithms that most GPS devices use will first assume that any vertical changes can be ignored, but continue up that slope for more than a few seconds and the smoothing algorithms will begin to incorporate the vertical rate of change too and the speed reported will reflect that.
Public GPS signals simply aren't accurate enough to do any reasonably accurate/contemporaneous determination of speed anyway, it's all a bit of a fudge. (Consider a 3m accuracy per reading and moving at 20mph =~ 9m/s. Two positions one second apart whilst moving at 9m/s could be reported as anything between 3m and 15m apart. The more points you smooth in the lower the error will be, but the slower the algorithm will be to responding to a change in velocity.)
If you have a wheel sensor available the GPS will use that augment the smoothing algorithms. It can't just trust the wheel size the user has input as this is (a) often wrong and (b) changes with tyre pressure. Indeed my Forerunner 935 doesn't even ask for a wheel size, it calculates it (and adjusts it) based on the GPS distance traveled and the number of wheel revolutions reported. The wheel sensor helps fill in the gaps where the GPS signal isn't strong enough (tree cover, tunnels, etc) or gives misleading values (due to reflections of buildings) compared to the expectation of moving steadily in roughly a straight line.
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Public GPS signals simply aren't accurate enough to do any reasonably accurate/contemporaneous determination of speed anyway, it's all a bit of a fudge. (Consider a 3m accuracy per reading and moving at 20mph =~ 9m/s. Two positions one second apart whilst moving at 9m/s could be reported as anything between 3m and 15m apart. The more points you smooth in the lower the error will be, but the slower the algorithm will be to responding to a change in velocity.)
AIUI this isn't how GPS speed works: It measures the doppler shift of the signal, rather than deriving from changes in position, and is therefore surprisingly accurate (as long as the signal's decent and you're not moving too erratically).
The wheel sensor is still advantageous for the reasons you mention, and because it works properly at low speeds (particularly 0) where it's hard to distinguish genuine movement from GPS error.
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Yes, should have been clearer. It was more about how GPS positional data alone can't be relied up for accurate velocity determination.
Here's a pretty good (but detailed) description of how it is done:
http://www.aprs.net/vm/gps_cs.htm
The most relevant section is:-
In early GPS receivers, four PRs from 4 satellites was converted into a 3-D (XYZ, Lat/Lon/Hgt or whatever) position plus the calibration of the timing bias of your receiver, and 4 PRRs were converted into a 3-D velocity plus a measurement of the frequency error of the oscillator. More modern receivers take all the PR+PRR data from all the N satellites in view for the past T seconds and feeds the 2*N*T PR+PRR samples it into a single mathematical "black box" (BB) (usually a Kalman filter) to produce an over- determined estimate of the same 8 parameters. So in modern receivers, this BB is using both the combination of past & present PRs and PRRs from many satellites to improve the Position, Velocity & Time (PVT) estimate. So Paul's statement about velocities being determined by changes in position is sorta, partially correct, but (when you look at the equations inside the BB), the measured "apparent Doppler" frequencies are even more important.
So velocity is going to be most heavily influenced by the doppler shift values (which aren't specific to the horizontal plane, i.e. speed will take into account the slope) but still takes recent positional updates into account albeit less significantly within the calculations.
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That still doesn't clearly demonstrate to me that it is taking speed from distance along the plane of the road vs distance on a flat xy grid imposed on the ground
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You are of course expressing an average speed and since it is not a linear relationship between speed and effort, you cannot just take that and multiple by some number to come up with an average "extra" effort. However, taking the output of one of the online calculators the estimate would be that for every hour you are cycling at 15mph into a 15mph headwind you will burn an extra 170 Calories over what you would burn if the wind was still.
Cool, you're suggesting an integral approach. I wish I could remember how to do that. ???
You'd need a Pitot tube on the bike for starters. Something like this (https://www.banggood.com/fr/PT60-Tube-Air-Speed-Meter-Sensor-Kit-Differential-for-Pixhawk-APM-PX4-Flight-Controller-RC-Airplane-p-1371068.html?gmcCountry=FR¤cy=EUR&createTmp=1&utm_source=googleshopping&utm_medium=cpc_union&utm_content=2zou&utm_campaign=ssc-fr-all-0302&ad_id=335402343736&gclid=Cj0KCQjwsZ3kBRCnARIsAIuAV_SxZKB8pbjqKiE9gX3pyxtjbpniU7bny6eWf-33TDYFbzUuGJIey1caArOSEALw_wcB&ID=522057&cur_warehouse=CN).
It'd need a bit of hacking, though...
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That still doesn't clearly demonstrate to me that it is taking speed from distance along the plane of the road vs distance on a flat xy grid imposed on the ground
From the page...
The Doppler shift includes the vector sum of the satellite's ~7 km/sec orbital velocity plus the 400 m/sec (at the equator) rotational velocity of the earth plus your receiver's motions (in a moving car, ~10-50 m/sec).
So, some of the inputs to the calculation are derived velocities (and positions) of known objects (the satellites) that massively dwarf the eventual computed velocity (10m/s) that it still manages to calculate accurately, and are in a whole load of random directions (each satellite will be moving in a completely different direction to the others at any one time).
For it to only compute the velocity in the horizontal plane (relative to the Earth's surface) it would have to compute the velocity of the device using this information (since it has no idea what the horizontal plane is at this point), then calculate where the device is on the Earth, what the horizontal plane is at that point (with reference to the geodetic datum), then calculate the vertical component of the velocity now it knows what 'horizontal' is, then recalculate the velocity of the device in the horizontal plane only and report that.
Or it could just use the original velocity it calculated.
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You'd need a Pitot tube on the bike for starters. Something like this (https://www.banggood.com/fr/PT60-Tube-Air-Speed-Meter-Sensor-Kit-Differential-for-Pixhawk-APM-PX4-Flight-Controller-RC-Airplane-p-1371068.html?gmcCountry=FR¤cy=EUR&createTmp=1&utm_source=googleshopping&utm_medium=cpc_union&utm_content=2zou&utm_campaign=ssc-fr-all-0302&ad_id=335402343736&gclid=Cj0KCQjwsZ3kBRCnARIsAIuAV_SxZKB8pbjqKiE9gX3pyxtjbpniU7bny6eWf-33TDYFbzUuGJIey1caArOSEALw_wcB&ID=522057&cur_warehouse=CN).
It'd need a bit of hacking, though...
It already exists:
https://m.probikekit.co.uk/cycling-power-meters/powerpod-powermeter-v2/11514777.html
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About bloody time, too.
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It gets a reasonable review from DC Rainmaker too: https://www.dcrainmaker.com/2016/03/powerpod-depth-review.html
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At that price I might have forked out for it a few years back but now I couldn't really justify it.
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I never got the PowerPod to work. Expensive paper weight.
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I never got the PowerPod to work. Expensive paper weight.
Mind if I swap it for another heavy object and see if I can make it work?
Round these parts, slogging into a headwind is basically par for the course, On my most recent headwind training session (Yes I am crazy enough to seek out a strong headwind for training!), a paired strava segment (2 segments for same stretch of road, but in each direction), it took me 20:54 in one direction, and 8:06 in the reverse, that was with winds 45+kph. The segment was 4.9km.
No tailwind will make up for the headwind you suffered to get there...
J
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Can a mechanics nerd explain to me why the power required to ride at 15 mph into a 15 mph headwind is much less than that needed to ride at 30 mph on a still day (ignoring non-aero forces)?
Surely from the reference frame of either the air or the bike the work being done is the same - why is the relative position of the earth relevant?
It seems the standard equation is this:
P = C * S * (S+H)^2
(Where S is ground speed, H is headwind and C is an aero drag constant)
Why is that not C * (S+H)^3? I'm sure the equation above is correct, I just can't get my head around *why* it is correct - what less work is being done?
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It's impossible to answer "why" questions - Why is Gravity?? - but we can probably help the keen student reach his/her own level of satisfaction :P
Two hints:
- what is the definition of "Work done"?
- Look at your equations, and consider the case of S=0.
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Can a mechanics nerd explain to me why the power required to ride at 15 mph into a 15 mph headwind is much less than that needed to ride at 30 mph on a still day (ignoring non-aero forces)?
Surely from the reference frame of either the air or the bike the work being done is the same - why is the relative position of the earth relevant?
It seems the standard equation is this:
P = C * S * (S+H)^2
(Where S is ground speed, H is headwind and C is an aero drag constant)
Why is that not C * (S+H)^3? I'm sure the equation above is correct, I just can't get my head around *why* it is correct - what less work is being done?
The effort required to overcome rolling resistance rises as a linear function of speed - riding at double the speed results in a considerable increase in output overcoming rolling resistance.
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- Look at your equations, and consider the case of S=0.
Having pondered this, I think the explanation I’m looking for is that in the headwind example, the wind is doing part of the work of moving the air past the rider, hence the rider needs to do less work than when they’re forcing their way through static air on the own.
effort required to overcome rolling resistance rises as a linear function of speed - riding at double the speed results in a considerable increase in output overcoming rolling resistance.
I’m looking at the equation for aero drag in isolation.
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It's really very simple.
In moving an object against a force, work done = force * distance travelled. Power is work per second, therefore it's force * speed.
In the case of 30mph in still air vs 15mph into 15mph wind, the force is the same in both cases, but the speed is halved in the 15mph case. Hence it requires half as much power.
Rolling resistance also comes into it, but is a much smaller factor at these kind of speeds.
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Please also note that wind speed is usually measured 10 meters above the ground. Wind speed drops significantly as you approach the ground with speed being 0 at the ground (boundary layers). As a rough approximation, wind speed is 1/2 that 1m above the ground than it is at 10m and 1m is where you, the dragiest part of the system reside. Essentially, 15mph quoted does not equal 15mph across your whole bike, if any of it.
Furthermore, it's rare that the wind hits you directly from the front. I'm slowly working my way through discussions from a chap called Hambini who reckons that yaw is much greater than previously suspected as he takes transient airflow into account instead of steady state that most people use.
With all this info, the equation of choice is D = Cd * A * 0.5 * r * V^2. Assuming air density, frontal area and coefficient of drag all stay the same, and if we assume that the wind is only half that measured at 10m (ie. 7.5mph), total velocity is increased by 50% to give a drag increase of 2.25x vs 4x at 30mph. Drag is directly proportional to required power output
So in summary, riding at 15mph into a "15mph" headwind will approximate to riding at 22.5mph.
*there's talk that a still day isn't a still day though, but let's not get into that....
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Please also note that wind speed is usually measured 10 meters above the ground. Wind speed drops significantly as you approach the ground with speed being 0 at the ground (boundary layers). As a rough approximation, wind speed is 1/2 that 1m above the ground that it is at 10m and 1m is where you, the dragiest part of the system reside.
The boundary effect makes a real difference to a low recumbent in windy conditions, even if it's not a particularly aerodynamic one (eg. tadpole trikes at the more touring end of the spectrum). Harder to quantify theoretically is the effect of being low enough to get meaningful shelter from even minimal roadside vegetation. Anecdotally, that makes a huge difference to crosswinds (as you get reminded every time you pass a field entrance).
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Please also note that wind speed is usually measured 10 meters above the ground. Wind speed drops significantly as you approach the ground with speed being 0 at the ground (boundary layers). As a rough approximation, wind speed is 1/2 that 1m above the ground that it is at 10m and 1m is where you, the dragiest part of the system reside.
The boundary effect makes a real difference to a low recumbent in windy conditions, even if it's not a particularly aerodynamic one (eg. tadpole trikes at the more touring end of the spectrum). Harder to quantify theoretically is the effect of being low enough to get meaningful shelter from even minimal roadside vegetation. Anecdotally, that makes a huge difference to crosswinds (as you get reminded every time you pass a field entrance).
I always think this makes sense, but am surprised that TT bikes don't tend to come with lower bottom brackets, and that riders don't seek out the lowest pedal system stack heights, to get themselves lower to the ground. Given the obsessive focus of testers on buying any speed going, anyone know why this isn't more of a thing?
Maybe I'll brave going back onto the TT forum and see what responses I get...
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Maybe they're worried about pedals striking the ground when cornering (I tend not to pedal through corners, but then I am not a racer). Or maybe the UCI has rules on the bottom bracket drop like they have on the position of the saddle?
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There must be a UCI rule in there somewhere, otherwise people would use low-racers.
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There are UCI rules about where the saddle can be wrt the BB, and where the aero extensions can be wrt the saddle and the head tube, so you end up with a bike that looks a lot like a bike and not a low-racer.
Whether there are any rules about dropping the BB down I don't know. There's only so far you can go though while retaining decent leg extension and avoiding pedal strike. I know at least one of the TTF crowd has experimented with reducing leg extension to get everything lower, but found the power loss too difficult to overcome.
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BB spindle must be 24-30 cm above the ground:
https://www.uci.org/docs/default-source/equipment/approval-protocol-eng.pdf?sfvrsn=c07e81c6_12
Given a wheel radius of 334 mm (700x23), that's a BB drop of 34-94mm. A quick google suggests the lowest TT BBs are 80mm drop, and most are 60-65mm, so it's probably not UCI rules that are limiting it. I guess you may run into other geometry limitations - head tube length, downtube clearance, etc as well as the pedal strike risk.
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There must be a UCI rule in there somewhere, otherwise people would use low-racers.
It's CTT, not UCI. There isn't a rule on BB height
https://www.cyclingtimetrials.org.uk/articles/view/11 (https://www.cyclingtimetrials.org.uk/articles/view/11)
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Maybe they're worried about pedals striking the ground when cornering (I tend not to pedal through corners, but then I am not a racer). Or maybe the UCI has rules on the bottom bracket drop like they have on the position of the saddle?
People take greater risks than a pedal strike on a roundabout in pursuit of speed. Most riders would trade-off a little bit of speed on roundabouts to go faster between them!
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People do indeed seek out low stack pedals. They also experiment with reduced leg extension, and of you look at TT pics from the last few years you'll see that a good proportion of riders have switched to running their saddles very far back so they get as low as possible while maintaining leg extension, albeit with a tighter hip angle. Basically they're trying to approximate a recumbent within the bicycle rules
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People do indeed seek out low stack pedals. They also experiment with reduced leg extension, and of you look at TT pics from the last few years you'll see that a good proportion of riders have switched to running their saddles very far back so they get as low as possible while maintaining leg extension, albeit with a tighter hip angle. Basically they're trying to approximate a recumbent within the bicycle rules
Yes, that happens but nobody seems to go on about low BB, and not many change pedals for lower stack.
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A headwind is good for the soul. And bugger all use for anything else.
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A headwind is good for the soul. And bugger all use for anything else.
Hill training, when you have no hills...
J
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A headwind is good for the soul. And bugger all use for anything else.
Hill training, when you have no hills...
J
That fits under the good for the soul category. If you get saintly enough you can float up the hills :facepalm: