Been meaning to query this group on subject information. Noticed that field sprints result in extreme back/forth leaning of bike frames as riders attempt to increase the power applied to crank. Also noticed similar techniques in time trials to a lesser degree and even road riding. Understand the purpose and concept, but the technique also seems to result in the wheel tracks following a zig-zag path rather than the shorter straight line distance to the finish line.
Has anyone done the math to prove that the added power applied to the crank results in a decrease in time to the finish line that is greater than the loss of time by riding a zig-zag path to the finish line? Would not the result of the extreme leaning be better if the zig-zagging was minimized, or even eliminated?
On Aug 2, 9:04 am, Gary Kunstmann <gkuns...@veawb.coop> wrote:
> Been meaning to query this group on subject information. Noticed that
> field sprints result in extreme back/forth leaning of bike frames as
> riders attempt to increase the power applied to crank. Also noticed
> similar techniques in time trials to a lesser degree and even road
> riding. Understand the purpose and concept, but the technique also
> seems to result in the wheel tracks following a zig-zag path rather than
> the shorter straight line distance to the finish line.
> Has anyone done the math to prove that the added power applied to the
> crank results in a decrease in time to the finish line that is greater
> than the loss of time by riding a zig-zag path to the finish line?
> Would not the result of the extreme leaning be better if the zig-zagging
> was minimized, or even eliminated?
I can't provide the power analysis you seek, but do have a comment to
help toward envisioning the complete picture.
Note that just because the wheels track a sinuous path does not
necessarily mean the rider's center of mass does. In fact the wheels
themselves don't even follow the same path.
So "loss of time by riding a zig-zag path" is at least partially
illusory. Not saying it doesn't exist just that it is probably much
less than casual observation might suggest. Watch, for example, a
rier's hips.
On Thursday, August 2, 2012 11:04:49 AM UTC-4, Gary Kunstmann wrote:
> Been meaning to query this group on subject information. Noticed that
> field sprints result in extreme back/forth leaning of bike frames as
> riders attempt to increase the power applied to crank. Also noticed
> similar techniques in time trials to a lesser degree and even road
> riding. Understand the purpose and concept, but the technique also
> seems to result in the wheel tracks following a zig-zag path rather than
> the shorter straight line distance to the finish line.
> Has anyone done the math to prove that the added power applied to the
> crank results in a decrease in time to the finish line that is greater
> than the loss of time by riding a zig-zag path to the finish line?
> Would not the result of the extreme leaning be better if the zig-zagging
> was minimized, or even eliminated?
I think the zig-zagging is not very pronounced. I think that if you viewed the tire tracks from the top, you'd see relatively small angles between the tire tracks and the intended direction.
Jobst frequently referred to "cosine error," i.e. that the cosine of a small angle is very close to 1. It applies here in that the angular deviation doesn't add much extra distance at all.
> On Thursday, August 2, 2012 11:04:49 AM UTC-4, Gary Kunstmann wrote:
> > Been meaning to query this group on subject information. Noticed that
> > field sprints result in extreme back/forth leaning of bike frames as
> > riders attempt to increase the power applied to crank. Also noticed
> > similar techniques in time trials to a lesser degree and even road
> > riding. Understand the purpose and concept, but the technique also
> > seems to result in the wheel tracks following a zig-zag path rather than
> > the shorter straight line distance to the finish line.
> > Has anyone done the math to prove that the added power applied to the
> > crank results in a decrease in time to the finish line that is greater
> > than the loss of time by riding a zig-zag path to the finish line?
> > Would not the result of the extreme leaning be better if the zig-zagging
> > was minimized, or even eliminated?
> I think the zig-zagging is not very pronounced.
Those who have actually ridden in such situations (or had their front
wheel taken out by a zigzaggy sprinter) know that the "lateral
component" can be QUITE pronounced, more so in "sprints" that involve
high torque efforts at slower speed, such as going uphill.
> I think that if you viewed the tire tracks from the top, you'd see relatively small angles between the tire tracks and the intended direction.
That is probably often true, especially at higher speeds.
DR
On Thursday, August 2, 2012 8:04:49 AM UTC-7, Gary Kunstmann wrote:
> Been meaning to query this group on subject information. Noticed that
> field sprints result in extreme back/forth leaning of bike frames as
> riders attempt to increase the power applied to crank. Also noticed
> similar techniques in time trials to a lesser degree and even road
> riding. Understand the purpose and concept...
I think maybe you misunderstand the purpose and concept. They're not tipping the bike in an *attempt* to increase power applied to the crank; they're tipping the bike to counterbalance the force they're *successfully* applying to the crank.
On Aug 2, 4:04 pm, Gary Kunstmann <gkuns...@veawb.coop> wrote:
> Been meaning to query this group on subject information. Noticed that
> field sprints result in extreme back/forth leaning of bike frames as
> riders attempt to increase the power applied to crank. Also noticed
> similar techniques in time trials to a lesser degree and even road
> riding. Understand the purpose and concept, but the technique also
> seems to result in the wheel tracks following a zig-zag path rather than
> the shorter straight line distance to the finish line.
> Has anyone done the math to prove that the added power applied to the
> crank results in a decrease in time to the finish line that is greater
> than the loss of time by riding a zig-zag path to the finish line?
> Would not the result of the extreme leaning be better if the zig-zagging
> was minimized, or even eliminated?
Lateral displacement of the wheels is generally instigated by them
being unstable. The rider tends to lock into the oscillation making
matters worse. It is not desirable and not to be confused with
deliberate blocking which mimimicks the behaviour of a sprinter with
unstable wheels in a more pronounced way. Racing rules should
disallow any rider with this exagerated action (wheels tracking wider
than shoulders) even if it does not hinder another as it may lead to a
fall so potentially causing unecessary injury. The style generally
should not be encouraged.
> > On Thursday, August 2, 2012 11:04:49 AM UTC-4, Gary Kunstmann wrote:
> > > Been meaning to query this group on subject information. Noticed that
> > > field sprints result in extreme back/forth leaning of bike frames as
> > > riders attempt to increase the power applied to crank. Also noticed
> > > similar techniques in time trials to a lesser degree and even road
> > > riding. Understand the purpose and concept, but the technique also
> > > seems to result in the wheel tracks following a zig-zag path rather than
> > > the shorter straight line distance to the finish line.
> > > Has anyone done the math to prove that the added power applied to the
> > > crank results in a decrease in time to the finish line that is greater
> > > than the loss of time by riding a zig-zag path to the finish line?
> > > Would not the result of the extreme leaning be better if the zig-zagging
> > > was minimized, or even eliminated?
> > I think the zig-zagging is not very pronounced.
> Those who have actually ridden in such situations (or had their front
> wheel taken out by a zigzaggy sprinter) know that the "lateral
> component" can be QUITE pronounced, more so in "sprints" that involve
> high torque efforts at slower speed, such as going uphill.
> > I think that if you viewed the tire tracks from the top, you'd see relatively small angles between the tire tracks and the intended direction.
> That is probably often true, especially at higher speeds.
> DR
It's actually very easy to estimate the zigzag path from an estimate
of the lateral deviation and minimal other assumptions.
Looking a video head- on it looks like a rider may commonly "sweep
out" a path .3m in width (~1 ft).
This full lateral excursion takes place within a pedal cycle (two
pedals strokes, R-L).
A single pedal stroke accounts for the entire lateral movement in one
direction. That same single pedal stroke accounts for 1/2 of the
distance the bike travels in a pedal cycle - also known as "gear
development."
So with these assumptions, we have measurement for the (1)lateral
deviation and over a section of the (2) non- straight path, i.e, two
sides of a right triangle.
Simple trig gives us the angle of deviation from straight is arcsin(.
3/4.77)- about 3°
And the ratio of the longer to straight is 4.77 / Sqr((4.77 ^ 2) -
(0.3 ^ 2))
Or 1.002
Changing only the gear - to 39/15, the same routine
gives 1.006
A small increase over the straight line in either case.
These are quickie calculations that assume straight lines rather than
the somewhat longer sinuous path that the wheel would actually be
following.
DirtRoadie wrote:
> On Aug 2, 12:19 pm, DirtRoadie <DirtRoa...@aol.com> wrote:
>> On Aug 2, 11:29 am, frkry...@gmail.com wrote:
>>> On Thursday, August 2, 2012 11:04:49 AM UTC-4, Gary Kunstmann wrote:
>>>> Been meaning to query this group on subject information. Noticed that
>>>> field sprints result in extreme back/forth leaning of bike frames as
>>>> riders attempt to increase the power applied to crank. Also noticed
>>>> similar techniques in time trials to a lesser degree and even road
>>>> riding. Understand the purpose and concept, but the technique also
>>>> seems to result in the wheel tracks following a zig-zag path rather than
>>>> the shorter straight line distance to the finish line.
>>>> Has anyone done the math to prove that the added power applied to the
>>>> crank results in a decrease in time to the finish line that is greater
>>>> than the loss of time by riding a zig-zag path to the finish line?
>>>> Would not the result of the extreme leaning be better if the zig-zagging
>>>> was minimized, or even eliminated?
>>> I think the zig-zagging is not very pronounced.
>> Those who have actually ridden in such situations (or had their front
>> wheel taken out by a zigzaggy sprinter) know that the "lateral
>> component" can be QUITE pronounced, more so in "sprints" that involve
>> high torque efforts at slower speed, such as going uphill.
>>> I think that if you viewed the tire tracks from the top, you'd see relatively small angles between the tire tracks and the intended direction.
>> That is probably often true, especially at higher speeds.
>> DR
> It's actually very easy to estimate the zigzag path from an estimate
> of the lateral deviation and minimal other assumptions.
> Looking a video head- on it looks like a rider may commonly "sweep
> out" a path .3m in width (~1 ft).
> This full lateral excursion takes place within a pedal cycle (two
> pedals strokes, R-L).
> A single pedal stroke accounts for the entire lateral movement in one
> direction. That same single pedal stroke accounts for 1/2 of the
> distance the bike travels in a pedal cycle - also known as "gear
> development."
> So with these assumptions, we have measurement for the (1)lateral
> deviation and over a section of the (2) non- straight path, i.e, two
> sides of a right triangle.
> Simple trig gives us the angle of deviation from straight is arcsin(.
> 3/4.77)- about 3�
> And the ratio of the longer to straight is 4.77 / Sqr((4.77 ^ 2) -
> (0.3 ^ 2))
> Or 1.002
> Changing only the gear - to 39/15, the same routine
> gives 1.006
> A small increase over the straight line in either case.
> These are quickie calculations that assume straight lines rather than
> the somewhat longer sinuous path that the wheel would actually be
> following.
> DR
Thanks! It seems like it could be nearing 1%. Well worth reducing effect by changing technique.
Gary Kunstmann <gkuns...@veawb.coop> writes:
> DirtRoadie wrote:
>> It's actually very easy to estimate the zigzag path from an estimate
>> of the lateral deviation and minimal other assumptions.
>> Looking a video head- on it looks like a rider may commonly "sweep
>> out" a path .3m in width (~1 ft).
>> This full lateral excursion takes place within a pedal cycle (two
>> pedals strokes, R-L).
>> A single pedal stroke accounts for the entire lateral movement in one
>> direction. That same single pedal stroke accounts for 1/2 of the
>> distance the bike travels in a pedal cycle - also known as "gear
>> development."
>> So with these assumptions, we have measurement for the (1)lateral
>> deviation and over a section of the (2) non- straight path, i.e, two
>> sides of a right triangle.
>> Simple trig gives us the angle of deviation from straight is arcsin(.
>> 3/4.77)- about 3°
>> And the ratio of the longer to straight is 4.77 / Sqr((4.77 ^ 2) -
>> (0.3 ^ 2))
>> Or 1.002
>> Changing only the gear - to 39/15, the same routine
>> gives 1.006
>> A small increase over the straight line in either case.
>> These are quickie calculations that assume straight lines rather than
>> the somewhat longer sinuous path that the wheel would actually be
>> following.
>> DR
> Thanks! It seems like it could be nearing 1%. Well worth reducing
> effect by changing technique.
Assuming the path is a sine wave, fractional increase in length is
approximately
dL/L = (pi/2*w/L)^2
where w = total width of path
L = forward length of one full revolution
Using w = 0.3 m
L = 9.54 m
gives
dL/L = 0.0024
which agrees nicely with DR's straight line approximation.
As noted, that represents the increase in the path of the contact patch of the
tire. The path of the rider through the air increases by a smaller value.
> Gary Kunstmann <gkuns...@veawb.coop> writes:
> > DirtRoadie wrote:
> >> It's actually very easy to estimate the zigzag path from an estimate
> >> of the lateral deviation and minimal other assumptions.
> >> Looking a video head- on it looks like a rider may commonly "sweep
> >> out" a path .3m in width (~1 ft).
> >> This full lateral excursion takes place within a pedal cycle (two
> >> pedals strokes, R-L).
> >> A single pedal stroke accounts for the entire lateral movement in one
> >> direction. That same single pedal stroke accounts for 1/2 of the
> >> distance the bike travels in a pedal cycle - also known as "gear
> >> development."
> >> So with these assumptions, we have measurement for the (1)lateral
> >> deviation and over a section of the (2) non- straight path, i.e, two
> >> sides of a right triangle.
> >> Simple trig gives us the angle of deviation from straight is arcsin(.
> >> 3/4.77)- about 3°
> >> And the ratio of the longer to straight is 4.77 / Sqr((4.77 ^ 2) -
> >> (0.3 ^ 2))
> >> Or 1.002
> >> Changing only the gear - to 39/15, the same routine
> >> gives 1.006
> >> A small increase over the straight line in either case.
> >> These are quickie calculations that assume straight lines rather than
> >> the somewhat longer sinuous path that the wheel would actually be
> >> following.
> >> DR
> > Thanks! It seems like it could be nearing 1%. Well worth reducing
> > effect by changing technique.
> Assuming the path is a sine wave, fractional increase in length is
> approximately
> dL/L = (pi/2*w/L)^2
> where w = total width of path
> L = forward length of one full revolution
> Using w = 0.3 m
> L = 9.54 m
> gives
> dL/L = 0.0024
> which agrees nicely with DR's straight line approximation.
> As noted, that represents the increase in the path of the contact patch of the
> tire. The path of the rider through the air increases by a smaller value.
> --
> Joe Riel
Thanks for fleshing that out. I thought you might.
There is a slight disparity which does not show up in the numbers.
I originally used the "development" as the straight line path (as you
did) until realizing that if we are assuming that the bike's wheels
are zigzagging then the rear wheel is traveling the longer ZZ path. No
matter. Whether solving for the hypotenuse or for the straight leg of
my right triangle the end result (ratio) is the same for the degree of
precision displayed here.
And if one really wants to split hairs, the rear wheel probably does
not deviate laterally as much as the front as we all should know from
tracks we leave after riding through a puddle.
So rather than worrying about the "ZZ factor" I suspect that it would
be more important to develop the general ability to avoid swerving or
veering - to get to the line quicker, to avoid collisions and to
avoid penalties or disqualifications.
DR
DirtRoadie <DirtRoa...@aol.com> writes:
> On Aug 3, 5:47 pm, Joe Riel <j...@san.rr.com> wrote:
>> Gary Kunstmann <gkuns...@veawb.coop> writes:
>> > DirtRoadie wrote:
>> >> It's actually very easy to estimate the zigzag path from an estimate
>> >> of the lateral deviation and minimal other assumptions.
>> >> Looking a video head- on it looks like a rider may commonly "sweep
>> >> out" a path .3m in width (~1 ft).
>> >> This full lateral excursion takes place within a pedal cycle (two
>> >> pedals strokes, R-L).
>> >> A single pedal stroke accounts for the entire lateral movement in one
>> >> direction. That same single pedal stroke accounts for 1/2 of the
>> >> distance the bike travels in a pedal cycle - also known as "gear
>> >> development."
>> >> So with these assumptions, we have measurement for the (1)lateral
>> >> deviation and over a section of the (2) non- straight path, i.e, two
>> >> sides of a right triangle.
>> >> Simple trig gives us the angle of deviation from straight is arcsin(.
>> >> 3/4.77)- about 3°
>> >> And the ratio of the longer to straight is 4.77 / Sqr((4.77 ^ 2) -
>> >> (0.3 ^ 2))
>> >> Or 1.002
>> >> Changing only the gear - to 39/15, the same routine
>> >> gives 1.006
>> >> A small increase over the straight line in either case.
>> >> These are quickie calculations that assume straight lines rather than
>> >> the somewhat longer sinuous path that the wheel would actually be
>> >> following.
>> >> DR
>> > Thanks! It seems like it could be nearing 1%. Well worth reducing
>> > effect by changing technique.
>> Assuming the path is a sine wave, fractional increase in length is
>> approximately
>> dL/L = (pi/2*w/L)^2
>> where w = total width of path
>> L = forward length of one full revolution
>> Using w = 0.3 m
>> L = 9.54 m
>> gives
>> dL/L = 0.0024
>> which agrees nicely with DR's straight line approximation.
>> As noted, that represents the increase in the path of the contact patch of the
>> tire. The path of the rider through the air increases by a smaller value.
>> --
>> Joe Riel
> Thanks for fleshing that out. I thought you might.
> There is a slight disparity which does not show up in the numbers.
> I originally used the "development" as the straight line path (as you
> did) until realizing that if we are assuming that the bike's wheels
> are zigzagging then the rear wheel is traveling the longer ZZ path. No
> matter. Whether solving for the hypotenuse or for the straight leg of
> my right triangle the end result (ratio) is the same for the degree of
> precision displayed here.
Yeah, I realized that when thinking about this shortly after posting
(usually that's when I notice the various errors I've introduced).
As you note, that error is small. Essentially it is the same as
approximating 1/(1-x) by 1+x for small x.
> And if one really wants to split hairs, the rear wheel probably does
> not deviate laterally as much as the front as we all should know from
> tracks we leave after riding through a puddle.
> DirtRoadie wrote:
> > On Aug 2, 12:19 pm, DirtRoadie <DirtRoa...@aol.com> wrote:
> >> On Aug 2, 11:29 am, frkry...@gmail.com wrote:
> >>> On Thursday, August 2, 2012 11:04:49 AM UTC-4, Gary Kunstmann wrote:
> >>>> Been meaning to query this group on subject information. Noticed that
> >>>> field sprints result in extreme back/forth leaning of bike frames as
> >>>> riders attempt to increase the power applied to crank. Also noticed
> >>>> similar techniques in time trials to a lesser degree and even road
> >>>> riding. Understand the purpose and concept, but the technique also
> >>>> seems to result in the wheel tracks following a zig-zag path rather than
> >>>> the shorter straight line distance to the finish line.
> >>>> Has anyone done the math to prove that the added power applied to the
> >>>> crank results in a decrease in time to the finish line that is greater
> >>>> than the loss of time by riding a zig-zag path to the finish line?
> >>>> Would not the result of the extreme leaning be better if the zig-zagging
> >>>> was minimized, or even eliminated?
> >>> I think the zig-zagging is not very pronounced.
> >> Those who have actually ridden in such situations (or had their front
> >> wheel taken out by a zigzaggy sprinter) know that the "lateral
> >> component" can be QUITE pronounced, more so in "sprints" that involve
> >> high torque efforts at slower speed, such as going uphill.
> >>> I think that if you viewed the tire tracks from the top, you'd see relatively small angles between the tire tracks and the intended direction.
> >> That is probably often true, especially at higher speeds.
> >> DR
> > It's actually very easy to estimate the zigzag path from an estimate
> > of the lateral deviation and minimal other assumptions.
> > Looking a video head- on it looks like a rider may commonly "sweep
> > out" a path .3m in width (~1 ft).
> > This full lateral excursion takes place within a pedal cycle (two
> > pedals strokes, R-L).
> > A single pedal stroke accounts for the entire lateral movement in one
> > direction. That same single pedal stroke accounts for 1/2 of the
> > distance the bike travels in a pedal cycle - also known as "gear
> > development."
> > So with these assumptions, we have measurement for the (1)lateral
> > deviation and over a section of the (2) non- straight path, i.e, two
> > sides of a right triangle.
> > Simple trig gives us the angle of deviation from straight is arcsin(.
> > 3/4.77)- about 3°
> > And the ratio of the longer to straight is 4.77 / Sqr((4.77 ^ 2) -
> > (0.3 ^ 2))
> > Or 1.002
> > Changing only the gear - to 39/15, the same routine
> > gives 1.006
> > A small increase over the straight line in either case.
> > These are quickie calculations that assume straight lines rather than
> > the somewhat longer sinuous path that the wheel would actually be
> > following.
> > DR
> Thanks! It seems like it could be nearing 1%. Well worth reducing
> effect by changing technique.
> DirtRoadie <DirtRoa...@aol.com> writes:
> > On Aug 3, 5:47 pm, Joe Riel <j...@san.rr.com> wrote:
> >> Gary Kunstmann <gkuns...@veawb.coop> writes:
> >> > DirtRoadie wrote:
> >> >> It's actually very easy to estimate the zigzag path from an estimate
> >> >> of the lateral deviation and minimal other assumptions.
> >> >> Looking a video head- on it looks like a rider may commonly "sweep
> >> >> out" a path .3m in width (~1 ft).
> >> >> This full lateral excursion takes place within a pedal cycle (two
> >> >> pedals strokes, R-L).
> >> >> A single pedal stroke accounts for the entire lateral movement in one
> >> >> direction. That same single pedal stroke accounts for 1/2 of the
> >> >> distance the bike travels in a pedal cycle - also known as "gear
> >> >> development."
> >> >> So with these assumptions, we have measurement for the (1)lateral
> >> >> deviation and over a section of the (2) non- straight path, i.e, two
> >> >> sides of a right triangle.
> >> >> Simple trig gives us the angle of deviation from straight is arcsin(.
> >> >> 3/4.77)- about 3°
> >> >> And the ratio of the longer to straight is 4.77 / Sqr((4.77 ^ 2) -
> >> >> (0.3 ^ 2))
> >> >> Or 1.002
> >> >> Changing only the gear - to 39/15, the same routine
> >> >> gives 1.006
> >> >> A small increase over the straight line in either case.
> >> >> These are quickie calculations that assume straight lines rather than
> >> >> the somewhat longer sinuous path that the wheel would actually be
> >> >> following.
> >> >> DR
> >> > Thanks! It seems like it could be nearing 1%. Well worth reducing
> >> > effect by changing technique.
> >> Assuming the path is a sine wave, fractional increase in length is
> >> approximately
> >> dL/L = (pi/2*w/L)^2
> >> where w = total width of path
> >> L = forward length of one full revolution
> >> Using w = 0.3 m
> >> L = 9.54 m
> >> gives
> >> dL/L = 0.0024
> >> which agrees nicely with DR's straight line approximation.
> >> As noted, that represents the increase in the path of the contact patch of the
> >> tire. The path of the rider through the air increases by a smaller value.
> >> --
> >> Joe Riel
> > Thanks for fleshing that out. I thought you might.
> > There is a slight disparity which does not show up in the numbers.
> > I originally used the "development" as the straight line path (as you
> > did) until realizing that if we are assuming that the bike's wheels
> > are zigzagging then the rear wheel is traveling the longer ZZ path. No
> > matter. Whether solving for the hypotenuse or for the straight leg of
> > my right triangle the end result (ratio) is the same for the degree of
> > precision displayed here.
> Yeah, I realized that when thinking about this shortly after posting
> (usually that's when I notice the various errors I've introduced).
> As you note, that error is small. Essentially it is the same as
> approximating 1/(1-x) by 1+x for small x.
> > And if one really wants to split hairs, the rear wheel probably does
> > not deviate laterally as much as the front as we all should know from
> > tracks we leave after riding through a puddle.
Okay, I wasn't *sprinting*, but I was tipping the bike side to side
pretty dramatically climbing a long grade yesterday on a narrow road
with essentially no paved shoulder but a white stripe at the road
edge. Not a lot of traffic but they don't want to follow a slow bike
up this long grade on their way home from work, so I ride *right* on
the white line. Tipping side to side to stay upright while applying
power off axis, I weaved a bit but stayed pretty much right on the
line.
But I wasn't staying on the line to maximize efficiency of propulsion;
I was doing it to show overtakign traffic that that was all the road I
needed and it was okay for them to pass carefully. For that matter,
efficiency itself has merit, but is not the holy grail.
Racers may politely listen to armchair analysts, and I suppose smart
ones will even give it due consideration, but when the race is on,
they do what they know in their bones will make the bike go fast.
