gravity works better on heavier objects... (was swb vs. GR, etc)

Discussion in 'Recumbent bicycles' started by Seth Jayson, Feb 11, 2003.

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  1. Seth Jayson

    Seth Jayson Guest

    Saw comments like this a few times in the long thread regarding rolldowns and coasting:

    (This one from Tom S.)

    "When riding my RANS Rocket, I am able to out-coast a riding companion on a front faired TiGRR from
    a near stop up to about 15 mph (~25 kph), but the TiGRR gains speed more rapidly after that. I
    believe that this is due to my gross weight being about 30 lbs. (~13 1/2 kgf) greater but my having
    a greater CdA. [1]"

    Now, last time I checked, gravity, even when diluted by, say, a hill, pulls objects with the same
    accelleration, no matter what their mass. (Remember Gallileo and his different orbs dropping from
    the window of the Church in Pisa?)

    Now, I remember back when building pinewood derby racers that we all seemed to think heavier was
    better too.

    Why this assumption? It seems to be pretty common

    Given the same equipment, running in a vaccuum, two bikes carrying different masses ought to have
    the same acceleration down the same slope.

    In the real world, where there's wind resistance, etc., do we start to see some advantage from
    greater mass in keeping our momentum against the wind?

    sj
     
    Tags:


  2. Rcpinto

    Rcpinto Guest

    Seth Jayson wrote;

    >Now, last time I checked, gravity, even when diluted by, say, a hill, pulls objects with the same
    >accelleration, no matter what their mass. (Remember Gallileo and his different orbs dropping from
    >the window of the Church in Pisa?)
    >

    Seth...IMO the easiest way to think about what is happening here is to think larger and smaller
    parachutes, and lighter and heavier objects, and what would happen if we varied the weight of an
    object, and the size of the attached parachute.

    If Gallileo (sp?) had thrown out two orbs of indentical total weight, but one had a parachute
    attached, the objects would not have reached the ground at the same time.

    The same thing happens in coastdowns- the "parachute" is the rider frontal area and rolling
    resistance. If you increase the frontal area or the rolling resistance- the "parachute", or
    retarding force, gets bigger.

    Those two retarding forces are offset by the force pulling the rider down the hill, which is
    the total weight of the vehicle multiplied by the % slope of the hill. So if you have a 200 lb
    total vehicle weight, and are on a 3% hill, you have 6 lbs of force pulling you down the hill.

    When you coast down that 3% hill on a 200 lb vehicle and you stop gaining speed, that means
    that the total retarding forces (aero, rolling resistance, bearing friction) are totaling 6
    lbs...you have reached terminal velocity.

    If you increase the weight of the vehicle, all else being equal, you *will* (1) reach a higher
    coastdown top speed, because the force pulling you down the hill is greater, and terminal
    velocity/top speed will increase.

    At analyticcycling.com, under "terminal velocity" if you use average recumbent values, and
    speeds between 20-30MPH, you'll see a good rule of thumb is 1% extra weight will result in an ~
    .5% higher terminal velocity.

    Rich Pinto
    Bacchetta Bicycles

    (1) I just wanted to try a Tom S footnote...I said *will* because the simple physics here are not
    negotiable ;<)
     
  3. AFAIK In the tdf, those water bottles handed out at the top of the mountain are full of lead shot.
    --
    Bill "Pop Pop" Patterson Retired and riding my Linear, my front drive low racer and our M5 tandem.
     
  4. At the risk of showing my "ignernse," I think you're both right.

    If I remember my high school physics correctly, Galileo showed that mass has no effect on the
    acceleration of a falling object. You wouldn't think that a piano and a bowling ball would fall at
    the same rate, but they do. (It's this desire to investigate seemingly intuitive concepts that got
    his butt excommunicated.) [1] Therefore, theoretically, I believe a 200 lb. bicyclist and a 2000 lb.
    bicyclist, all things (frontal area, rolling resistance, etc.) being equal, would accelerate at the
    same speed down an identical hill. I suppose you could test this if you were able to find a 2000 lb.
    bicyclist with the same frontal area as the 200 lb. bicyclist, an identically-sized bicycle that
    would support him or her, the bazillion PSI tires that would give them the same contact patch size,
    blah blah blah.

    However, Mr. Pinto must design his excellent bicycles to function in the real world. In this world,
    air density matters, which is why it's included in the analyticcyling.com calculations that Mr.
    Pinto cites.

    Even when using the same rider and the same bike over the same course, I think minute differences in
    frontal area, rolling resistance, and other factors during individual rolldown tests make it
    impossible to reach anything more substantive than broad conclusions. (Maybe one guy sneezes during
    a trial and the reverse thrust alters his acceleration.) One of the posters -- Mr. Delaire,
    perhaps-- alluded to this when he said that all these parameters interact in ways that are hard to
    put into words. That's why I've stopped working about such insignificant factors and am now focusing
    on more important factors, such as "On which bike does my wife think I look the most sexy?"

    Andrew

    [1] Yay! Footnote! Wasn't there some footage of one of the Apollo astronauts dropping a rock and a
    feather on the moon and they dropped at the same rate?

    "RCPINTO" <[email protected]> wrote in message news:[email protected]...
    > Seth Jayson wrote;
    >
    >
    > >Now, last time I checked, gravity, even when diluted by, say, a hill, pulls objects with the same
    > >accelleration, no matter what their mass. (Remember Gallileo and his different orbs dropping from
    > >the window of the Church in Pisa?)
    > >
    >
    > Seth...IMO the easiest way to think about what is happening here is to think larger and
    > smaller parachutes, and lighter and heavier objects, and
    what
    > would happen if we varied the weight of an object, and the size of the
    attached
    > parachute.
    >
    > If Gallileo (sp?) had thrown out two orbs of indentical total weight,
    but
    > one had a parachute attached, the objects would not have reached the
    ground at
    > the same time.
    >
    > The same thing happens in coastdowns- the "parachute" is the rider
    frontal
    > area and rolling resistance. If you increase the frontal area or the
    rolling
    > resistance- the "parachute", or retarding force, gets bigger.
    >
    > Those two retarding forces are offset by the force pulling the rider
    down
    > the hill, which is the total weight of the vehicle multiplied by the %
    slope of
    > the hill. So if you have a 200 lb total vehicle weight, and are on a 3%
    hill,
    > you have 6 lbs of force pulling you down the hill.
    >
    > When you coast down that 3% hill on a 200 lb vehicle and you stop
    gaining
    > speed, that means that the total retarding forces (aero, rolling
    resistance,
    > bearing friction) are totaling 6 lbs...you have reached terminal velocity.
    >
    > If you increase the weight of the vehicle, all else being equal, you *will* (1) reach a
    > higher coastdown top speed, because the force pulling
    you
    > down the hill is greater, and terminal velocity/top speed will increase.
    >
    > At analyticcycling.com, under "terminal velocity" if you use average
    > recumbent values, and speeds between 20-30MPH, you'll see a good rule of
    thumb
    > is 1% extra weight will result in an ~ .5% higher terminal velocity.
    >
    > Rich Pinto
    > Bacchetta Bicycles
    >
    > (1) I just wanted to try a Tom S footnote...I said *will* because the
    simple
    > physics here are not negotiable ;<)
    >
    >
    >
     
  5. Alpha Beta

    Alpha Beta Guest

    When they go down hill, they put on descent jerseys. The should make them out of lead threading.

    "Bill Patterson" <[email protected]> wrote in message news:[email protected]...
    > AFAIK In the tdf, those water bottles handed out at the top of the mountain are full of lead shot.
     
  6. In article <[email protected]>, [email protected] says...
    > Saw comments like this a few times in the long thread regarding rolldowns and coasting:
    >
    > (This one from Tom S.)
    >
    > "When riding my RANS Rocket, I am able to out-coast a riding companion on a front faired TiGRR
    > from a near stop up to about 15 mph (~25 kph), but the TiGRR gains speed more rapidly after that.
    > I believe that this is due to my gross weight being about 30 lbs. (~13 1/2 kgf) greater but my
    > having a greater CdA. [1]"
    >
    > Now, last time I checked, gravity, even when diluted by, say, a hill, pulls objects with the same
    > accelleration, no matter what their mass. (Remember Gallileo and his different orbs dropping from
    > the window of the Church in Pisa?)
    >
    > Now, I remember back when building pinewood derby racers that we all seemed to think heavier was
    > better too.
    >
    > Why this assumption? It seems to be pretty common
    >
    > Given the same equipment, running in a vaccuum, two bikes carrying different masses ought to have
    > the same acceleration down the same slope.
    >
    > In the real world, where there's wind resistance, etc., do we start to see some advantage from
    > greater mass in keeping our momentum against the wind?
    >
    > sj
    >

    True - acceleration is constant for the two masses - 9.8 m/s/s. This is why, in a vacuum, the
    feather and the steel ball fall at the same speed. When wind resistance is introduced you must look
    at the energy equation for a simple solution.

    The heavier rider at the top of the hill has accumulated more potential energy (mgh) than the
    lighter rider and thus has more to dissipate to drag losses. You could also look at it as a force
    equation but this is more complicated. In any case, the heavier rider is faster down the hill all
    other things being equal (like frontal area).

    Of course, by the same token, the lighter rider is to the top of the hill first and no, these
    advantages/disadvantages do not cancel out in the long run as drag losses at higher speeds (where
    the heavier person has the advantages) are "lossier" than weight advantages in climbing since drag
    energy losses increase with the cube of the speed. In sum - all other things being equal, the
    lighter rider has the advantage - but we knew that anyway.

    Regards Chris
     
  7. "Andrew Heckman" <[email protected]> wrote in message
    news:[email protected]...

    > (Maybe one guy sneezes during a trial and the reverse thrust alters his acceleration.)

    Hey - there's the argument for riding DF's!
     
  8. Seth Jayson

    Seth Jayson Guest

    OK, cool, that's about what I suspected (but did not word very nicely).

    I remember doing some experiments back in high school and college where we proved that lighter was
    faster down the hill (the hill being a ramp in a room, and the bike being some smaller contraptions)
    because the light object produced less friction. Obviously, in that case, there was no air
    resistance to worry about.

    I'm assuming that any weight differences between riders on bikes will have very little influence
    on the friction in the bike/rider/road system. (Especially when compared to the big impact of air
    at speed.)

    But anyone have any ideas how, say, bad bearings, lack of grease, might impede acceleration? (This
    is a bonus question for real geeks only.)

    sj
     
  9. Rich, Your ruining my day. Since I have gained a few pounds...well more than a few I have to drag it
    up the hill. Now you tell me that since my frontal area has increased also....I get no gain from the
    added weight on the downhill.

    Damm...I hate this science stuff. It ruins my rationalization.

    Jude....///Bacchetta AERO St. Michaels and Tilghman Island.. Maryland Wheel Doctor Cycle and Sports,
    Inc 1-800-586-6645 "RCPINTO" <[email protected]> wrote in message
    news:[email protected]...
    > >OK, cool, that's about what I suspected (but did not word very nicely).
    > >
    > >I remember doing some experiments back in high school and college where we proved that lighter
    > >was faster down the hill (the hill being a ramp in a room, and the bike being some smaller
    > >contraptions) because the light object produced less friction. Obviously, in that case, there was
    > >no air resistance to worry about.
    > >
    > >I'm assuming that any weight differences between riders on bikes will have very little influence
    > >on the friction in the bike/rider/road system. (Especially when compared to the big impact of air
    > >at speed.)
    > >
    > >But anyone have any ideas how, say, bad bearings, lack of grease, might impede acceleration?
    > >(This is a bonus question for real geeks only.)
    > >
    > >sj
    > >
    >
    >
    > Seth
    >
    > All the parameters involved in these experiments are absolutely quantifiable and have been
    > completely understood (and used in all sorts of engineering and science) for many hundreds of
    > years.
    >
    > When it comes to effects of extra weight on a bicycle, the main drag effect, if all else
    > stays equal, will be to increase tire rolling
    resistance,
    > which is proportional to the load on the tires. If you increase the
    weight of
    > the vehicle 10%, the rolling resistance will go up 10%.
    >
    > And, if all else is equal, 10% extra weight will cause about a 5%
    increase
    > in coastdown speeds at 20-30 MPH.
    >
    > As far as bearing drag goes, most bicycle science references have it
    as
    > less than 1% of the total drag in most cases. I sure very badly
    maintained
    > bikes can be a lot higher.
    >
    > A much higher loss would be between the crank and the rear wheel,
    where
    > depending on chain tensions mostly, transmission losses can be as high as
    15%,
    > or as low as 2-3%.
    >
    >
    > Rich "Real Geek" Pinto
    > Bacchetta Bicycles
     
  10. It may not be as bad is it sounds, Jude. Excess pie and BEER consumption leads to extra mass, but it
    tends to stick out in front, rather than to the side. Hence not only is there no increase in frontal
    area, but the so-called "aerobelly" effect may even improve the drag coefficient of the rig.

    ;-)

    Dave Larrington - http://legslarry.crosswinds.net/
    ===========================================================
    Editor - British Human Power Club Newsletter
    http://www.bhpc.org.uk/
    ===========================================================
     
  11. Hi Rich Math is a useful tool in prediction of physics though it is not always exact or accurate.
    Remember that the mathematicians once predicted top speed for a human powered vehicle on flat ground
    to be 65 mph. Modern bikes have clocked 80 mph! An error of 20%? What was left out of the equation?
    This is why it is important to do the tests. 1% weight increase will not equal .5% speed increase in
    the real world. In my case, a full, large water bottle would equal a 1% percent increase in total
    bike/rider weight. I'm curious so it will be tested. Happy cycling Steve "Speedy" Delaire

    RCPINTO wrote:

    > >At the risk of showing my "ignernse," I think you're both right.
    > >
    > >If I remember my high school physics correctly, Galileo showed that mass has no effect on the
    > >acceleration of a falling object. You wouldn't think that a piano and a bowling ball would fall
    > >at the same rate, but they do. (It's this desire to investigate seemingly intuitive concepts that
    > >got his butt excommunicated.)
    >
    > Hi Andrew
    >
    > I hate to be picky...but...that Galileo experiment is probably the most misunderstood legendary
    > experiments in science.
    >
    > As far as the bowling ball and the piano falling at exactly at the same rate- this would happen
    > *only* in a vacuum. The piano will likely have a higher aero drag per pound (larger parachute
    > per pound) and would hit the ground very slightly after the bowling ball.
    >
    > >1] Therefore, theoretically, I believe a 200 lb. bicyclist
    > >and a 2000 lb. bicyclist, all things (frontal area, rolling resistance, etc.) being equal, would
    > >accelerate at the same speed down an identical hill. I suppose you could test this if you were
    > >able to find a 2000 lb. bicyclist with the same frontal area as the 200 lb. bicyclist, an
    > >identically-sized bicycle that would support him or her, the bazillion PSI tires that would give
    > >them the same contact patch size, blah blah blah.
    > >
    >
    > If you could find an identical frontal area bicycle and rider (with average bent values for
    > frontal area and RR) but one weighed 200 lbs and one weighed 2000 lbs, on a 3% slope...the
    > heavier rider would coastdown at ~42 meters per second (94 MPH) and the 200 lb rider would
    > coastdown at 13.7 m/sec
    > (30.6 MPH)...over 300% faster for the heavier rider. Once again, all at analyticcyling.com, under
    > "terminal velocity".
    >
    > Because the numbers were so outlandish in this example, it did vary from the rule of thumb I
    > gave for most coastdowns at 20-30Mph - if you add 1% to the weight of an average bicycle in
    > a 20-30 coastdown- the coastdown speed WILL increase ~.5%.
    >
    > Rich Pinto
    > Bacchetta Bicycles
    >
    >

    -----= Posted via Newsfeeds.Com, Uncensored Usenet News =----- http://www.newsfeeds.com - The #1
    Newsgroup Service in the World! -----== Over 80,000 Newsgroups - 16 Different Servers! =-----
     
  12. Seth Jayson

    Seth Jayson Guest

    "Torben Scheel" <[email protected]> wrote in message news:<[email protected]>...
    > "Andrew Heckman" <[email protected]> wrote in message
    > news:[email protected]...
    >
    > > (Maybe one guy sneezes during a trial and the reverse thrust alters his acceleration.)
    >
    > Hey - there's the argument for riding DF's!

    This upward thrust (from the downward head position of the DF rider) could cause a momentary,
    catostrophic loss of control as the force lifts you off your tires and reduces your control.

    Alway hold in your sneezes in the hopes that they may:
    a) pass out your ears, cancelling each other out.
    b) pass out somewhere else (toward the rear?) thereby giving you an advantage.
     
  13. Dave, With the seat at 25 degrees gravity causes my "aerobelly" to sag to the side and it becomes
    "speedbraken lovehandle".

    Jude....///Bacchetta AERO St. Michaels and Tilghman Island.. Maryland Wheel Doctor Cycle and Sports,
    Inc 1-800-586-6645 "Dave Larrington" <[email protected]> wrote in message
    news:[email protected]...
    > It may not be as bad is it sounds, Jude. Excess pie and BEER consumption leads to extra mass, but
    > it tends to stick out in front, rather than to
    the
    > side. Hence not only is there no increase in frontal area, but the so-called "aerobelly" effect
    > may even improve the drag coefficient of the rig.
    >
    > ;-)
    >
    > Dave Larrington - http://legslarry.crosswinds.net/
    > ===========================================================
    > Editor - British Human Power Club Newsletter
    > http://www.bhpc.org.uk/
    > ===========================================================
     
  14. >> I hate to be picky...but...that Galileo experiment is probably the most
    misunderstood legendary experiments in science.<<

    Go ahead, be picky! It'd be a pretty boring newsgroup otherwise!

    >>As far as the bowling ball and the piano falling at exactly at the same
    rate- this would happen *only* in a vacuum. The piano will likely have a higher aero drag per pound
    (larger parachute per pound) and would hit the ground very slightly after the bowling ball.<<

    I guess what I was trying to get at was that, *THEORETICALLY*, if both the bicyclists had the same
    size "parachute," they'd descent at the same rate regardless of mass. But in the real world (as
    opposed to in a vacuum where gravity would be the only force at work), everything has a parachute.

    This stuff is why I minored in physics rather than majored. Jeez, I hate that pesky math!
    "Aerobellys" are a lot more fun!

    "RCPINTO" <[email protected]> wrote in message news:[email protected]...
    > >At the risk of showing my "ignernse," I think you're both right.
    > >
    > >If I remember my high school physics correctly, Galileo showed that mass
    has
    > >no effect on the acceleration of a falling object. You wouldn't think
    that a
    > >piano and a bowling ball would fall at the same rate, but they do. (It's this desire to
    > >investigate seemingly intuitive concepts that got his butt excommunicated.)
    >
    > Hi Andrew
    >
    > I hate to be picky...but...that Galileo experiment is probably the most misunderstood legendary
    > experiments in science.
    >
    > As far as the bowling ball and the piano falling at exactly at the same rate- this would happen
    > *only* in a vacuum. The piano will likely have a higher aero drag per pound (larger parachute
    > per pound) and would hit the ground very slightly after the bowling ball.
    >
    >
    >
    > >1] Therefore, theoretically, I believe a 200 lb. bicyclist
    > >and a 2000 lb. bicyclist, all things (frontal area, rolling resistance, etc.) being equal, would
    > >accelerate at the same speed down an identical hill. I suppose you could test this if you were
    > >able to find a 2000 lb. bicyclist with the same frontal area as the 200 lb. bicyclist, an
    > >identically-sized bicycle that would support him or her, the bazillion
    PSI
    > >tires that would give them the same contact patch size, blah blah blah.
    > >
    >
    > If you could find an identical frontal area bicycle and rider (with average bent values for
    > frontal area and RR) but one weighed 200 lbs and
    one
    > weighed 2000 lbs, on a 3% slope...the heavier rider would coastdown at
    ~42
    > meters per second (94 MPH) and the 200 lb rider would coastdown at 13.7
    m/sec
    > (30.6 MPH)...over 300% faster for the heavier rider. Once again, all at analyticcyling.com, under
    > "terminal velocity".
    >
    > Because the numbers were so outlandish in this example, it did vary
    from
    > the rule of thumb I gave for most coastdowns at 20-30Mph - if you add 1%
    to the
    > weight of an average bicycle in a 20-30 coastdown- the coastdown speed
    WILL
    > increase ~.5%.
    >
    >
    > Rich Pinto
    > Bacchetta Bicycles
     
  15. "Andrew Heckman" skrev...
    > This stuff is why I minored in physics rather than majored. Jeez, I hate that pesky math!
    > "Aerobellys" are a lot more fun!

    Gravity sucks. Thats all you need to know. ;-)

    Mikael
     
  16. Dave Lehnen

    Dave Lehnen Guest

    Seth Jayson wrote:

    >Saw comments like this a few times in the long thread regarding rolldowns and coasting:
    >
    >(This one from Tom S.)
    >
    >"When riding my RANS Rocket, I am able to out-coast a riding companion on a front faired TiGRR from
    >a near stop up to about 15 mph (~25 kph), but the TiGRR gains speed more rapidly after that. I
    >believe that this is due to my gross weight being about 30 lbs. (~13 1/2 kgf) greater but my having
    >a greater CdA. [1]"
    >
    >Now, last time I checked, gravity, even when diluted by, say, a hill, pulls objects with the same
    >accelleration, no matter what their mass. (Remember Gallileo and his different orbs dropping from
    >the window of the Church in Pisa?)
    >
    If Gallileo could have looked closely enough, the heavier cannonball (or whatever it was) would have
    hit the ground very slightly ahead of the smaller, lighter one. This is because the mass increases
    with the cube of the diameter, but the frontal area only with the square of the diameter. For a
    fairly short fall, with dense, heavy objects, the difference was too small for him to see. In a
    vacuum they would be dead even. At the other extreme, compare a falling sack of flour to individual
    single particles of flour (dust).

    >
    >Now, I remember back when building pinewood derby racers that we all seemed to think heavier was
    >better too.
    >
    >Why this assumption? It seems to be pretty common
    >
    >Given the same equipment, running in a vaccuum, two bikes carrying different masses ought to have
    >the same acceleration down the same slope.
    >
    >In the real world, where there's wind resistance, etc., do we start to see some advantage from
    >greater mass in keeping our momentum against the wind?
    >
    >sj
    >
    >
    Wind resistance is a major effect on bicycles, not one that can safely be neglected. With both
    people and cannonballs, weight increases more quickly than frontal area, and other things being
    roughly equal, heavy riders will out-coast light ones down a hill.

    Dave Lehnen
     
  17. Seth Jayson

    Seth Jayson Guest

    higher.
    >
    > A much higher loss would be between the crank and the rear wheel, where depending on chain
    > tensions mostly, transmission losses can be as high as 15%, or as low as 2-3%. (Bacchetta
    > Rich)

    So wait, you're telling me I need to tune and grease my Campy Record stuff? I thought I was buying
    efficiency up front!

    Interesting data on weight's benefit fighting air on the downhills.

    Maybe you folks at Bacchetta can add sandbags to your accessories section. ;)

    (Maybe some kind of contract for people to provide them at the top of big hills while we're on
    tour...) I mean, with a 22 pound Ti 'bent (and I have neither gut nor butt, thanks to Mom's genes)
    how am I supposed to get moving down the hills?

    Oh, and if I might ask, how do you folks at the big B pronounce your firm's name? I speak Italian,
    and my instinct is to ask bike shop owners about their Bah-Kettas (Italian pronunciation),
    especially considering that all your bike names are Italian. They always look at me like I'm a nut.
    On the other hand, they do say Jee-roh, and not Gee-roh...
     
  18. Tom Sherman

    Tom Sherman Guest

    Dave Lehnen wrote:
    >
    > ... If Gallileo could have looked closely enough, the heavier cannonball > (or whatever it was)...

    Being an intelligent man, I believe Galileo Gallili would have had his assistant on the ground
    getting a close look at the cannonballs landing while he was dropping them out of the tower. ;)

    Tom Sherman - Quad Cities USA (Illinois side) Various HPV's
     
  19. Mark Milam

    Mark Milam Guest

    [email protected] (RCPINTO) wrote in message news:<[email protected]>...
    > >> A much higher loss would be between the crank and the rear wheel,
    > where
    > >> depending on chain tensions mostly, transmission losses can be as high as
    > 15%,
    > >> or as low as 2-3%.
    > >> (Bacchetta Rich)
    > >
    So, How do I get 2-3%, instead of 15%. Do I go with the smallest cog in the rear on the Ti Aero, and
    use the middle chainring or the Large Chainring and the 15 gear in the rear? Coming up on 1000 miles
    on the Aero and Love it. Mark Milam Lafayette, LA GRR, Ti Aero, Screamer
     
  20. Paul Bruneau

    Paul Bruneau Guest

    S. Delaire "Rotatorrecumbent" wrote:
    > Hi Rich Math is a useful tool in prediction of physics though it is not always exact or accurate.
    > Remember that the mathematicians once predicted top speed for a human powered vehicle on flat
    > ground to be 65 mph.

    If that's true, it wasn't a failure of math. It was a failure of the people making the predictions.
    I don't see how mathematics could be used to determine something like top speed on an hpv.
     
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