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Today I used tried out my new back wheel pannier for the
first time to carry home some groceries on my bike. I felt
a weir sensation when going on level ground. It took much
less pedaling power to get going quickly, and stay at that
speed than usual.
This got me thinking about gliders
and how adding extra
weight actually improves their speed. It's a trade off of
course. By carrying that extra weight, the glider can fly
faster, while maintaining the same glide ratio as before.
The down side is that if you find a source of lift, you won't
be able to utilize it as well and it will take longer to gain a
given altitude.
On a bike it is very similar. Finding lift means going up
hill. Gliding means going down hill. If a bike carried water
ballast, it would be tougher to go up hill, but on flat or
even down sloping terrain, I can't help to think that there
would an advantage. I'll need help to crunch the actual
numbers, but my thinking is along these lines. While
carrying 0 kg ballast, you can comfortably sustain 30
km/h. While carrying 20kg ballast, you can sustain
perhaps 33 km/h.
Before you fish this by saying, "ya, but it takes you much
more effort to get to the 33km/h in the first place". My
answer is that for a sufficiently long journey without many
starts and stops, this may actually be more energy
efficient.
I'm sorry that I can't provide the hard math to prove it.
This idea is partially a question to the engineers out there
- how would you calculate the trade off between, power
applied to the pedals, inertia, wind resistance, and tire
friction?
On a glider, the result ends up looking like a upside down U
when plotted on a sink rate/speed graph. This helps the
pilots pick the optimal ballast for the conditions. Weak lift
+ short journey = no ballast. Strong lift + long journey =
lots of ballast. I'm wondering if something similar is
possible for a bike. Lots of hills + starts and stops = no
ballast. Long journey + against the wind + no hills =
ballast.
bicycle with speed governor
bicycle_20with_20speed_20governor
my first idea on HB [xaviergisz, Sep 14 2009]
rolling resistance
http://en.wikipedia.../Rolling_resistance
Normal force is a multiplier of the coefficient [Sparkyplugclean, Sep 16 2009]
Lots of the math is provided for you here
http://en.wikipedia...Bicycle_performance
[21 Quest, Sep 16 2009, last modified Sep 17 2009]
[link]
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Wind resistance goes up with the cube of speed, no
matter what. So even if the extra inertia helps you
maintain your speed better, you're putting more energy in
to do it. Plus rolling resistance increases linearly with
weight, so you're losing more energy there.
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That cube of the speed thing also means that the slow
climbing is more efficient (in terms of total energy of the
bicycle rider system) than the fast downhill. Thus the
energy expended to climb a hill is always more than the
energy recovered going down the far side. Since the more
weight you're carrying, the more energy you spend going
up, more weight equals a much higher total expenditure.
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The net result is that more weight is not a good thing
under any circumstances except going down hill, and there
it's offset by the climbing in the first place. There's a
reason why good climbers are either skinny guys or guys
with legs that resemble battleship guns.
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What the extra inertia does is smooth out your power
input. Thus if you have a stomping pedal motion, or lots
of very small ups and downs it's a lot easier to glide over
them without noticing, but you're still putting more
energy in. |
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.... downhill maybe, on the flats no way. A bicycle isn't a glider and so there really is no correlation. All you noticed was that the heavier load rolled further for a given speed and that you could exert yourself then relax which feels easier to the less hardcore rider. |
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After all that's been said, I'd just like to point out that there's a
reason that hardcore riders (at least, the ones with money) shell
out the money for multithousand dollar bicycles that are made
of ultralight materials like titanium, magnesium, and carbon
fiber. |
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...and, as [MechE] says, the "King of the Mountains" cyclists in major events are always the thin, wirey guys, not the guys who have all the power and speed. |
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// I felt a weir sensation //
Stay away from weirs on your bicycle.
Perhaps you should propose a system of ballast stations at the top of all downhill sections. |
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//a system of ballast stations at the top of all downhill sections// Presumably, to avoid stopping, they use well-aimed hosepipes to fill your ballast tanks? |
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If the weir had been full you would have had your empirical evidence at the end of that journey. |
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I like thinking of a road course that is generally downhill, but with smaller hills on it. It would be a good feeling to not have to pedal at all on these sections. Also for those (like myself) that bike to and from work/school each day on a path that is defined as mostyl uphill or mostly downhill, one could, for example, fill up ballast tanks in the morning, coast faster and easier to the destination, empty and return uphill as normal. [+]. |
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//ballast..downhill// well-aimed hosepipes and those jokers that always spray me with them.
My ballast bags were full on the downhill, and that poor pedestrian... well, I just couldn't stop. |
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Ok I admit, I was way too optimistic by including
flats as one of the possible scenario. In my
defense, I did explain that I don't know what the
trade off is and what the actual "benefit"
scenarios are.
Here is a thought experiment: There are two
cloned racers (same physical ability) weighing 60
KG. One with state of the art light weight bike at
7 KG (total 67 KG). The other with a bicycle
equipped
with a water ballast system that adds adds extra
40 KG inside the aerodynamic frame of the bike
(107 KG total). Who will win? I guess more
accurately, who will win with what slope?
On one extreme, with the slope being nearly level,
the light bike would win. What about the other
extreme? 90 degree drop straight down? In that
case terminal velocity comes into play. Please
correct my calculations .. this is the first time I've
calculated anything like this in a while:
C=0.8 (drag coefficient estimate)
m=67 and 107 kg respectively
g=9.81 m/s^2 (they are on earth)
p=1.2 kg/m^3 (approx density of air)
A=0.3 m^2 (approx projected area)
Vt=SQRT(2mg/pAC)
Vt-heavy=307 Km/h
Vt-light=243 Km/h
Clearly, the heavy bike kicked some serious ass.
Now unless these people had a parachute they are
dead. I can't wrap my head around doing a
calculation for a more reasonable slope taking into
account rolling friction etc. One of the biggest
obstacles to that calculation is that I don't know
how to take slope into account for rolling friction.
For example, the wheel friction on a level slope
will be higher than on a 89.9 degree slope (i'm only
guessing I need some trig function to take that
into account) ... help! ...
... wild guess... is it F=CN * cos( down_hill_angle ) ?
?? |
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Weight helps on a smooth downhill, but other then the
aforementioned good and bad commute directions (or
free-ride mountain biking) you never have a pure downhill.
Free Riders slow down because of the difficulty of rough
terrain downhilling.
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Commuters slow down because of pavement. I have hit 64
kph on a downhill, but only with the advantage of seeing
several riders in front of me to pick out a clean line. At
those speeds, a small piece of gravel can be dangerous, a
large piece, or worse a blown front tire can be deadly. And
those speeds can be attained by fairly light riders on a
relatively moderate downhill. This might gain something
on very moderate (1-2% grades) downhills, but only there,
by 4-5% most people will be reaching for the brakes not
extra speed. (5% is 5 meters in 100, or about a 3 degree
downslope. Major roads rarely go above 6%, minor roads
rarely go above 8% or 5 degrees).
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The only people who are going to go that fast routinely (or
faster) are racers who had to climb to get there first. Also,
at high speeds, a nice tight aerodynamic tuck is going to
do you more good than extra weight. The equivalent to
shaving off 1-2 pounds in a climb, or adding it in a downhill
is a projection into the air stream the size of a pencil, end
on.
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A state of the art bike these days is closer to 3-5 kilos, and
there's a reason for that. |
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The pros get ultralight bikes because they know their course isn't all downhill. The heavy bike kicks ass down hill. I have a mountain bike and have coasted past fellow riders on lighter road bikes downhill without any extra effort. It's a disadvantage uphill, and breaks even on flat. Anything improved by retention of momentum is equally lost by difficulty of acceleration. There's no such thing as a free lunch. |
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Also, acceleration due to gravity on a slope is the component
along the slope, friction involves the component of weight
into the slope, so the acceleration will be the sine of the
slope angle, the rolling friction will be the cosine. Rolling
friction is pretty much negligible compared to air resistance
above about 20 kph though, so the decreased acceleration
due to gravity in the terminal velocity equation is your major
player, and remember, you're probably dealing with a less
than 10% down angle. |
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[Jelly] if the road bike riders go into a full aero tuck, they'll
blow past you. Wind is more important than weight. |
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Another factor that affects downhill speed is our old friend
Friction. Racing bikes have very skinny tires that cut through the
air and create minimal friction on the road surface. On a
downhill, racers usually will let the guy with the heavier bike
blast past them because they're taking the coast as an
opportunity to rest and conserve energy for the flats and climbs
later on. Aerodynamics and friction are on the side of the lighter
bike, and had your fellow riders so desired, they could've easily
smoked your mountain bike going any direction on pavement.
Your mountain bike has wide tires with aggressive treads
designed to dig into dirt and avoid bogging down when riding
offroad. The frame is heavy because it is thicker and designed to
take more of a pounding. |
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On a paved road, a lightweight road bike will beat a mountain
bike any day, any way, pending rider motivation. Personally, I
commute through the city on a medium trail bike. It's lighter and
faster than a mountain bike, but heavy enough to take the
punishment I put it through from jumping curbs and cutting
across grassy islands. I crashed head-on into a staircase a few
weeks ago when I got cocky, and while the inner tube blew and
the rim bent, the forks were fine. Such a collision would've likely
demolished a road bike. |
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In my earlier youth, I rode/hitchhiked an old "waterpipe" ten-speed from San Diego to San Francisco and back. |
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At one point in the hills above Santa Barbara, I was downhilling it fast and furious carrying fifty pounds of luggage, in a tight tuck seated on the rear rack with my chin on the seat,when a Ford Pinto pulled up next to me, rolled down the window, and shouted "Sixty-five! I thought you might like to know!" and moved on. |
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I do remember thinking that if anything went wrong it would hurt. In your early twenties that's negotiable. |
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Can I ask why my earlier trebuchet anno was deleted?
Whilst the trebuchet may have been flippant, I think the comment about peak density of water at 277K utterly relevant. |
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[coprocephalous] ... I definitely didn't delete it. Not
sure who else has the rights to do that. |
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//There's no such thing as a free lunch.//
Just wanted to point out that I'm keenly aware of
that. I should have written more background into
the idea, but the glider ballast I'm mentioning is
jettisonable. You can start with 200 KG water
ballast in your wings and if conditions change, or
when ready to land jettison all or part of your
ballast. This is the assumption for the bike water
ballast system too. The aerodynamic profile of a
bike with 50 KG water ballast would be equivalent
to that carrying 0 KG. All that would change is the
mass. That's why I find any references to "blowing
past your competitor if you tuck in more"
irrelevant since that's a constant. Both bikes and
both riders have the same wind resistance, only
one can start with a full tank of ballast on top of a
hill and then jettison it at the bottom ready for
the next climb.
Also in my opinion these anecdotal stories are fun
and interesting. But, what's the math behind this?
Can someone actually calculate who will win, on
what surface, with which watter ballast?
Obviously I showed that during free fall, ballast
wins - at what downhill grade does this cease
being the case? |
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Ixnaum, the point is this: what you'd gain in momentum would be lost with increased friction from the extra weight pressing the wheels harder against the ground. Gliders don't have that limitation, so it works for them. I believe it was Newton (although I could be wrong here) who proved that, if you drop an apple and a bowling ball from the same height they will reach the ground at the same time. I just confirmed this with a full can of soda and a cheap plastic Happy Meal toy. The weight has nothing to do with it. |
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The aero tuck comment was in response to mountain bike vs road, not directly to the idea. The major point of my comment above is that safety concerns with regard to speed will kick in well before the heavier cyclist starts winning. Actually doing the math is difficult, because there are so many factors involved. Even if you cancel everything out though, and ignore rolling friction, the equation becomes simply Vt=Sqrt[2m sin(slope)g/pAV]. What becomes critical is determining how long of a slope it takes to reach terminal velocity on a , being generous, 10 degree down slope.
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[MechE] thank you very much for that formula.
This is what I got:
Vt=Sqrt[2m sin(slope)g/pAV]
0.5% grade: Vt_heavy = 21 Km/h, Vt_light = 17
Km/h
1.0% grade: Vt_heavy = 30 Km/h, Vt_light = 24
Km/h
2.0% grade: Vt_heavy = 53 Km/h, Vt_light = 42
Km/h
5.0% grade: Vt_heavy = 68 Km/h, Vt_light = 54
Km/h
Notice that that's a constant improvement by a
factor of 1.26 (not bad at all). Now,
as you mentioned, at lower speed rolling friction
DOES become increasing component. So this
constant improvement will not hold for sure, it will
be slightly lower for lower road gradients. In a
race where seconds count, I can't help to think
that the jettisonable ballast would give a rider an
edge ... |
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I should add, that of course on say a 0.5% grade the
cyclists would still be pedaling, because they are
nowhere near a "dangerous" speed for the
conditions. However, that 1.26 improvement factor
means that one rider pedals less hard, and/or
can get into perfect aero-tuck position since they
are not pedaling as much and not disturbing their
form. |
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If the ride starts at the top of a hill, and you can truly find a way to add a significant amount of ballast without a) affecting the aerodynamics of the bike and b) increasing the base weight of the bike once the ballast is drained or dropped (this includes undrained liquid, then there is some benefit to this. I don't think you're going to find any cyclists who want to try it though.
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Other than downhill mountain biking I'm not aware of any cycling which is all down hill, and in free ride, terminal velocity is defined as the speed at which you hit that tree, nothing to do with wind resistance. |
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I'm pretty sure that the benefits gliders get from added ballast is due in some way either to their lack of rolling friction, or the fact that some other vehicle takes them up before they begin their descent. |
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Does anyone know what terminal velocity on a bike is? I'm not sure but I'm pretty sure it's above what a sensible rider would chance anyway. I went about 55 down the side of a paved mountain once and had only noticed that the wind was becoming a danger to my staying on the bike. |
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ixnaum's calculations are pretty close, it is weight
dependent. |
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Nice observation in the annos that you can harness the feather vs hammer effect. Bun [+]. |
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