Physics of dips

Quoted message said:

Every day, I pedal back into town on a smooth, paved country road that
runs along the bluffs above the Arkansas River.

The road is about as straight and level as a bowling alley--I can see
the sole traffic light almost a mile away.

But the road dips twice as it crosses the heads of small gullies.

Each dip is roughly enough to hide a single-story house.

Assuming that I'm doing 20 mph on the flat part of the road (usually a
little over that), and assuming that I put out the same effort (maybe
I try harder?) . . .

What should happen to my overall speed?

Do I go faster, slower, or the same speed for the whole mile when I
roller-coaster through these two dips, compared to what I'd do if the
whole road was flat?

Usually, my speed rises to 25 mph by the bottom of the dip and then
reaches 27-30 mph as I start climbing the far side. (Speedometer lag?)
By the time that I climb back up to the level road again, the speed is
back down to about 20 mph again.

It seems as if the climb should cancel the drop, but the speedometer
seems to show only a rise above 20 mph and a fall back to 20 mph.

Is this just because I get excited about going faster down into the
dip, pedal harder and tuck in without realizing it, and then work even
harder climbing back up out of the dip?

That would make me feel better about conservation of energy, but it's
hard to believe that I've got an extra 5-7 mph tucked up my sleeve
every day.

Carl Fogel

Now it seems even worse.

There I am, going a steady 20 mph on the level.

If I drop into a dip, my speed rises to say 25 mph by the bottom, and
then drops back down to 20 just as I reach the top. Obviously, my
average speed is faster.

If I reverse the dip and turn it into a little hill, then my speed
drops to say 15 at the top of the rise, and then increases back to 20
at the bottom. Obviously, my average speed is lower.

So dips increase my speed and little hills reduce it?

Something still seems fishy about this.

CF

Quoted message said:

Quoted message said:

Every day, I pedal back into town on a smooth, paved country road that
runs along the bluffs above the Arkansas River.

The road is about as straight and level as a bowling alley--I can see
the sole traffic light almost a mile away.

But the road dips twice as it crosses the heads of small gullies.

Each dip is roughly enough to hide a single-story house.

Assuming that I'm doing 20 mph on the flat part of the road (usually a
little over that), and assuming that I put out the same effort (maybe
I try harder?) . . .

What should happen to my overall speed?

Do I go faster, slower, or the same speed for the whole mile when I
roller-coaster through these two dips, compared to what I'd do if the
whole road was flat?

Usually, my speed rises to 25 mph by the bottom of the dip and then
reaches 27-30 mph as I start climbing the far side. (Speedometer lag?)
By the time that I climb back up to the level road again, the speed is
back down to about 20 mph again.

It seems as if the climb should cancel the drop, but the speedometer
seems to show only a rise above 20 mph and a fall back to 20 mph.

Is this just because I get excited about going faster down into the
dip, pedal harder and tuck in without realizing it, and then work even
harder climbing back up out of the dip?

That would make me feel better about conservation of energy, but it's
hard to believe that I've got an extra 5-7 mph tucked up my sleeve
every day.

Carl Fogel

Now it seems even worse.

There I am, going a steady 20 mph on the level.

If I drop into a dip, my speed rises to say 25 mph by the bottom, and
then drops back down to 20 just as I reach the top. Obviously, my
average speed is faster.

If I reverse the dip and turn it into a little hill, then my speed
drops to say 15 at the top of the rise, and then increases back to 20
at the bottom. Obviously, my average speed is lower.

So dips increase my speed and little hills reduce it?

Something still seems fishy about this.

CF

Aaargh!

Consider a much wider dip and wider hill.

At 20 mph on the flat, I descend, getting up to 25 mph.

My speed gradually slows back down to a steady 20 mph in the wide
bottom of the dip.

Then I reach the far side, start climbing, and my speed drops to say
15 mph by the time I reach the top.

My speed gradually rises back to 20 mph.

The gain should cancel the loss.

The same would seem to be true for a wide-top mesa-style hill.

I approach the foot of the climb at 20 mph, slow down to say 15 mph as
I reach the top, and gradually speed back up to 20 mph again across
the wide, flat top of the hill.

Then I dive down over the edge, speed up to 25 mph as I reach the
bottom again, and gradually slow back down to 20 mph.

The loss should cancel the gain.

This seems to contradict the short-dip and short-hill theory.

Aaargh!

CF

Quoted message said:

Quoted message said:

Quoted message said:

Every day, I pedal back into town on a smooth, paved country road that
runs along the bluffs above the Arkansas River.

The road is about as straight and level as a bowling alley--I can see
the sole traffic light almost a mile away.

But the road dips twice as it crosses the heads of small gullies.

Each dip is roughly enough to hide a single-story house.

Assuming that I'm doing 20 mph on the flat part of the road (usually a
little over that), and assuming that I put out the same effort (maybe
I try harder?) . . .

What should happen to my overall speed?

Do I go faster, slower, or the same speed for the whole mile when I
roller-coaster through these two dips, compared to what I'd do if the
whole road was flat?

Usually, my speed rises to 25 mph by the bottom of the dip and then
reaches 27-30 mph as I start climbing the far side. (Speedometer lag?)
By the time that I climb back up to the level road again, the speed is
back down to about 20 mph again.

It seems as if the climb should cancel the drop, but the speedometer
seems to show only a rise above 20 mph and a fall back to 20 mph.

Is this just because I get excited about going faster down into the
dip, pedal harder and tuck in without realizing it, and then work even
harder climbing back up out of the dip?

That would make me feel better about conservation of energy, but it's
hard to believe that I've got an extra 5-7 mph tucked up my sleeve
every day.

Carl Fogel

Now it seems even worse.

There I am, going a steady 20 mph on the level.

If I drop into a dip, my speed rises to say 25 mph by the bottom, and
then drops back down to 20 just as I reach the top. Obviously, my
average speed is faster.

If I reverse the dip and turn it into a little hill, then my speed
drops to say 15 at the top of the rise, and then increases back to 20
at the bottom. Obviously, my average speed is lower.

So dips increase my speed and little hills reduce it?

Something still seems fishy about this.

CF

Aaargh!

Consider a much wider dip and wider hill.

At 20 mph on the flat, I descend, getting up to 25 mph.

My speed gradually slows back down to a steady 20 mph in the wide
bottom of the dip.

Then I reach the far side, start climbing, and my speed drops to say
15 mph by the time I reach the top.

My speed gradually rises back to 20 mph.

The gain should cancel the loss.

The same would seem to be true for a wide-top mesa-style hill.

I approach the foot of the climb at 20 mph, slow down to say 15 mph as
I reach the top, and gradually speed back up to 20 mph again across
the wide, flat top of the hill.

Then I dive down over the edge, speed up to 25 mph as I reach the
bottom again, and gradually slow back down to 20 mph.

The loss should cancel the gain.

This seems to contradict the short-dip and short-hill theory.

Aaargh!

CF

Hmmm . . . maybe with a short enough dip or hill, a pendulum-style
effect outweighs wind-drag effect?

In a short enough dip, the 5-mph gained descending into the dip is
used quickly for climbing back up the far side instead of slowly bled
off by wind drag?

CF

Carl Fogel said:

Every day, I pedal back into town on a smooth, paved country road
that runs along the bluffs above the Arkansas River.

Quoted message said:

The road is about as straight and level as a bowling alley--I can
see the sole traffic light almost a mile away.

Quoted message said:

But the road dips twice as it crosses the heads of small gullies.

Quoted message said:

Each dip is roughly enough to hide a single-story house.

Quoted message said:

Assuming that I'm doing 20 mph on the flat part of the road (usually
a little over that), and assuming that I put out the same effort
(maybe I try harder?)...

Quoted message said:

What should happen to my overall speed?

That's the old "ramp and the ball" quiz for mechanical engineers.
You have a ramp followed by a straight level run to a timing device.
One configuration has a dip on the level part, the other does not.
Which ball gets there sooner?

The average speed of the one with the dip is greater so it will arrive
first... but the end velocity of the one arriving first is lower
because at greater speed more power is given up to air drag, both
paths having the same original energy input from the fixed length
ramp.

On a bicycle, where wind losses are substantial, the same thing occurs
except that the final velocity is lower (or rider work is greater).
We have such a place locally and it was fun to see that graphically
displayed. The rider who took the dip got back on the main (parallel)
road ahead of the rider who went on the level but he was distinctly
slower.

Quoted message said:

Do I go faster, slower, or the same speed for the whole mile when I
roller-coaster through these two dips, compared to what I'd do if the
whole road was flat?

Quoted message said:

Usually, my speed rises to 25 mph by the bottom of the dip and then
reaches 27-30 mph as I start climbing the far side. (Speedometer
lag?) By the time that I climb back up to the level road again, the
speed is back down to about 20 mph again.

I think you should have seen the answer already from your observations.

Quoted message said:

It seems as if the climb should cancel the drop, but the speedometer
seems to show only a rise above 20 mph and a fall back to 20 mph.

You are interfering with the process if you pedal hard.

Quoted message said:

Is this just because I get excited about going faster down into the
dip, pedal harder and tuck in without realizing it, and then work
even harder climbing back up out of the dip?

Quoted message said:

That would make me feel better about conservation of energy, but
it's hard to believe that I've got an extra 5-7 mph tucked up my
sleeve every day.

You're losing!

Jobst Brandt

Quoted message said:

Carl Fogel said:

Every day, I pedal back into town on a smooth, paved country road
that runs along the bluffs above the Arkansas River.

Quoted message said:

The road is about as straight and level as a bowling alley--I can
see the sole traffic light almost a mile away.

Quoted message said:

But the road dips twice as it crosses the heads of small gullies.

Quoted message said:

Each dip is roughly enough to hide a single-story house.

Quoted message said:

Assuming that I'm doing 20 mph on the flat part of the road (usually
a little over that), and assuming that I put out the same effort
(maybe I try harder?)...

Quoted message said:

What should happen to my overall speed?

That's the old "ramp and the ball" quiz for mechanical engineers.
You have a ramp followed by a straight level run to a timing device.
One configuration has a dip on the level part, the other does not.
Which ball gets there sooner?

The average speed of the one with the dip is greater so it will arrive
first... but the end velocity of the one arriving first is lower
because at greater speed more power is given up to air drag, both
paths having the same original energy input from the fixed length
ramp.

On a bicycle, where wind losses are substantial, the same thing occurs
except that the final velocity is lower (or rider work is greater).
We have such a place locally and it was fun to see that graphically
displayed. The rider who took the dip got back on the main (parallel)
road ahead of the rider who went on the level but he was distinctly
slower.

Quoted message said:

Do I go faster, slower, or the same speed for the whole mile when I
roller-coaster through these two dips, compared to what I'd do if the
whole road was flat?

Quoted message said:

Usually, my speed rises to 25 mph by the bottom of the dip and then
reaches 27-30 mph as I start climbing the far side. (Speedometer
lag?) By the time that I climb back up to the level road again, the
speed is back down to about 20 mph again.

I think you should have seen the answer already from your observations.

Quoted message said:

It seems as if the climb should cancel the drop, but the speedometer
seems to show only a rise above 20 mph and a fall back to 20 mph.

You are interfering with the process if you pedal hard.

Quoted message said:

Is this just because I get excited about going faster down into the
dip, pedal harder and tuck in without realizing it, and then work
even harder climbing back up out of the dip?

Quoted message said:

That would make me feel better about conservation of energy, but
it's hard to believe that I've got an extra 5-7 mph tucked up my
sleeve every day.

You're losing!

Jobst Brandt

Dear Jobst,

If I'm following you, you expect a no-extra-effort, no-better-tuck
rider to drop into the dip and climb back out sooner that he'd cover
the same distance on the flats (higher average speed), but to be going
slower at that point (lower exit speed)?

20mph. . . . . . . . . . 10 seconds

20mph. . . . . . less than 10 seconds, arrives sooner
. .
. .

20mph. . . . . . . . . . same 20 mph

20mph. . . . . . less than 20 mph
. .
. .

Does it mattter that the bicycle has enough steady power to produce 20
mph on the level, though it's greatly affected by wind drag, while the
ball isn't powered throughout the run and is probably far less
affected by wind drag?

And does the length of the dip and the entry speed matter? That is,
could there be a short enough dip that the rider still exits the dip
sooner but much closer to the same entry speed?

I can try to maintain the same posture to eliminate tuck, but I don't
see how to tell if I'm subconsciously cheating by pushing harder on
the pedals--the speed rises quite quickly from around 20 to around
25-27 mph, most of which I sadly attribute to gravity.

How wide and deep is that nice dip where you can compare riders?

And what does the rolling ball demo predict for rolling over a short
hill instead of a short dip? Does it still reach the level runout on
the far side sooner (higher average speed) but with a lower exit
speed?

Sorry if I'm misunderstanding you. Off to look for more about the
rolling ball on the internet.

Thanks,

Carl Fogel

Quoted message said:

Quoted message said:

Carl Fogel said:

Every day, I pedal back into town on a smooth, paved country road
that runs along the bluffs above the Arkansas River.

Quoted message said:

The road is about as straight and level as a bowling alley--I can
see the sole traffic light almost a mile away.

Quoted message said:

But the road dips twice as it crosses the heads of small gullies.

Quoted message said:

Each dip is roughly enough to hide a single-story house.

Quoted message said:

Assuming that I'm doing 20 mph on the flat part of the road (usually
a little over that), and assuming that I put out the same effort
(maybe I try harder?)...

Quoted message said:

What should happen to my overall speed?

That's the old "ramp and the ball" quiz for mechanical engineers.
You have a ramp followed by a straight level run to a timing device.
One configuration has a dip on the level part, the other does not.
Which ball gets there sooner?

The average speed of the one with the dip is greater so it will arrive
first... but the end velocity of the one arriving first is lower
because at greater speed more power is given up to air drag, both
paths having the same original energy input from the fixed length
ramp.

On a bicycle, where wind losses are substantial, the same thing occurs
except that the final velocity is lower (or rider work is greater).
We have such a place locally and it was fun to see that graphically
displayed. The rider who took the dip got back on the main (parallel)
road ahead of the rider who went on the level but he was distinctly
slower.

Quoted message said:

Do I go faster, slower, or the same speed for the whole mile when I
roller-coaster through these two dips, compared to what I'd do if the
whole road was flat?

Quoted message said:

Usually, my speed rises to 25 mph by the bottom of the dip and then
reaches 27-30 mph as I start climbing the far side. (Speedometer
lag?) By the time that I climb back up to the level road again, the
speed is back down to about 20 mph again.

I think you should have seen the answer already from your observations.

Quoted message said:

It seems as if the climb should cancel the drop, but the speedometer
seems to show only a rise above 20 mph and a fall back to 20 mph.

You are interfering with the process if you pedal hard.

Quoted message said:

Is this just because I get excited about going faster down into the
dip, pedal harder and tuck in without realizing it, and then work
even harder climbing back up out of the dip?

Quoted message said:

That would make me feel better about conservation of energy, but
it's hard to believe that I've got an extra 5-7 mph tucked up my
sleeve every day.

You're losing!

Jobst Brandt

Dear Jobst,

If I'm following you, you expect a no-extra-effort, no-better-tuck
rider to drop into the dip and climb back out sooner that he'd cover
the same distance on the flats (higher average speed), but to be going
slower at that point (lower exit speed)?

20mph. . . . . . . . . . 10 seconds

20mph. . . . . . less than 10 seconds, arrives sooner
. .
. .

20mph. . . . . . . . . . same 20 mph

20mph. . . . . . less than 20 mph
. .
. .

Does it mattter that the bicycle has enough steady power to produce 20
mph on the level, though it's greatly affected by wind drag, while the
ball isn't powered throughout the run and is probably far less
affected by wind drag?

And does the length of the dip and the entry speed matter? That is,
could there be a short enough dip that the rider still exits the dip
sooner but much closer to the same entry speed?

I can try to maintain the same posture to eliminate tuck, but I don't
see how to tell if I'm subconsciously cheating by pushing harder on
the pedals--the speed rises quite quickly from around 20 to around
25-27 mph, most of which I sadly attribute to gravity.

How wide and deep is that nice dip where you can compare riders?

And what does the rolling ball demo predict for rolling over a short
hill instead of a short dip? Does it still reach the level runout on
the far side sooner (higher average speed) but with a lower exit
speed?

Sorry if I'm misunderstanding you. Off to look for more about the
rolling ball on the internet.

Thanks,

Carl Fogel

That didn't take long:

http://www.schulphysik.de/ntnujava/racingBall/racingBall.html

The ball going through the dip wins the race, but I'm not sure what
the exit speeds are.

CF

Quoted message said:

Is this just because I get excited about going faster down into the
dip, pedal harder and tuck in without realizing it, and then work even
harder climbing back up out of the dip?

Yes.

Greg

--
"All my time I spent in heaven
Revelries of dance and wine
Waking to the sound of laughter
Up I'd rise and kiss the sky" - The Mekons

Quoted message said:

Quoted message said:

Every day, I pedal back into town on a smooth, paved country road that
runs along the bluffs above the Arkansas River.

The road is about as straight and level as a bowling alley--I can see
the sole traffic light almost a mile away.

But the road dips twice as it crosses the heads of small gullies.

Each dip is roughly enough to hide a single-story house.

Assuming that I'm doing 20 mph on the flat part of the road (usually a
little over that), and assuming that I put out the same effort (maybe
I try harder?) . . .

What should happen to my overall speed?

Do I go faster, slower, or the same speed for the whole mile when I
roller-coaster through these two dips, compared to what I'd do if the
whole road was flat?

Usually, my speed rises to 25 mph by the bottom of the dip and then
reaches 27-30 mph as I start climbing the far side. (Speedometer lag?)
By the time that I climb back up to the level road again, the speed is
back down to about 20 mph again.

It seems as if the climb should cancel the drop, but the speedometer
seems to show only a rise above 20 mph and a fall back to 20 mph.

Is this just because I get excited about going faster down into the
dip, pedal harder and tuck in without realizing it, and then work even
harder climbing back up out of the dip?

That would make me feel better about conservation of energy, but it's
hard to believe that I've got an extra 5-7 mph tucked up my sleeve
every day.

Carl Fogel

Now it seems even worse.

There I am, going a steady 20 mph on the level.

If I drop into a dip, my speed rises to say 25 mph by the bottom, and
then drops back down to 20 just as I reach the top. Obviously, my
average speed is faster.

http://www.physicalgeography.net/fundamentals/6e.html

If you're going 20 mph before the dip, then you're not going 20 mph when
you leave the dip unless you put more energy into the effort of getting
out of the dip.

Quoted message said:

If I reverse the dip and turn it into a little hill, then my speed
drops to say 15 at the top of the rise, and then increases back to 20
at the bottom. Obviously, my average speed is lower.

Slightly. If you're not going faster than 20 mph at the bottom of the
hill then you were riding the brakes or scrubbing energy in some other
manner.

Quoted message said:

So dips increase my speed and little hills reduce it?

They both decrease it. But you knew that.

Greg
--
"All my time I spent in heaven
Revelries of dance and wine
Waking to the sound of laughter
Up I'd rise and kiss the sky" - The Mekons

Quoted message said:

Quoted message said:

Quoted message said:

Carl Fogel writes:

> Every day, I pedal back into town on a smooth, paved country road
> that runs along the bluffs above the Arkansas River.

> The road is about as straight and level as a bowling alley--I can
> see the sole traffic light almost a mile away.

> But the road dips twice as it crosses the heads of small gullies.

> Each dip is roughly enough to hide a single-story house.

> Assuming that I'm doing 20 mph on the flat part of the road (usually
> a little over that), and assuming that I put out the same effort
> (maybe I try harder?)...

> What should happen to my overall speed?

That's the old "ramp and the ball" quiz for mechanical engineers.
You have a ramp followed by a straight level run to a timing device.
One configuration has a dip on the level part, the other does not.
Which ball gets there sooner?

The average speed of the one with the dip is greater so it will arrive
first... but the end velocity of the one arriving first is lower
because at greater speed more power is given up to air drag, both
paths having the same original energy input from the fixed length
ramp.

On a bicycle, where wind losses are substantial, the same thing occurs
except that the final velocity is lower (or rider work is greater).
We have such a place locally and it was fun to see that graphically
displayed. The rider who took the dip got back on the main (parallel)
road ahead of the rider who went on the level but he was distinctly
slower.

> Do I go faster, slower, or the same speed for the whole mile when I
> roller-coaster through these two dips, compared to what I'd do if the
> whole road was flat?

> Usually, my speed rises to 25 mph by the bottom of the dip and then
> reaches 27-30 mph as I start climbing the far side. (Speedometer
> lag?) By the time that I climb back up to the level road again, the
> speed is back down to about 20 mph again.

I think you should have seen the answer already from your observations.

> It seems as if the climb should cancel the drop, but the speedometer
> seems to show only a rise above 20 mph and a fall back to 20 mph.

You are interfering with the process if you pedal hard.

> Is this just because I get excited about going faster down into the
> dip, pedal harder and tuck in without realizing it, and then work
> even harder climbing back up out of the dip?

> That would make me feel better about conservation of energy, but
> it's hard to believe that I've got an extra 5-7 mph tucked up my
> sleeve every day.

You're losing!

Jobst Brandt

Dear Jobst,

If I'm following you, you expect a no-extra-effort, no-better-tuck
rider to drop into the dip and climb back out sooner that he'd cover
the same distance on the flats (higher average speed), but to be going
slower at that point (lower exit speed)?

20mph. . . . . . . . . . 10 seconds

20mph. . . . . . less than 10 seconds, arrives sooner
. .
. .

20mph. . . . . . . . . . same 20 mph

20mph. . . . . . less than 20 mph
. .
. .

Does it mattter that the bicycle has enough steady power to produce 20
mph on the level, though it's greatly affected by wind drag, while the
ball isn't powered throughout the run and is probably far less
affected by wind drag?

And does the length of the dip and the entry speed matter? That is,
could there be a short enough dip that the rider still exits the dip
sooner but much closer to the same entry speed?

I can try to maintain the same posture to eliminate tuck, but I don't
see how to tell if I'm subconsciously cheating by pushing harder on
the pedals--the speed rises quite quickly from around 20 to around
25-27 mph, most of which I sadly attribute to gravity.

How wide and deep is that nice dip where you can compare riders?

And what does the rolling ball demo predict for rolling over a short
hill instead of a short dip? Does it still reach the level runout on
the far side sooner (higher average speed) but with a lower exit
speed?

Sorry if I'm misunderstanding you. Off to look for more about the
rolling ball on the internet.

Thanks,

Carl Fogel

That didn't take long:

http://www.schulphysik.de/ntnujava/racingBall/racingBall.html

The ball going through the dip wins the race, but I'm not sure what
the exit speeds are.

CF

And some more:

http://www.physics.umd.edu/lecdem/services/demos/demosc2/c2-11.htm

This one is more psychology and addresses how people view and explain
various animations of the balls:

http://groups.physics.umn.edu/physed/People/Tom%20Koch/2_tracks/

This one says that the ball going through the dip returns to its
original speed, not a lower speed:

http://www.physics.umd.edu/lecdem/outreach/QOTW/arch1/q002.htm

CF

On Fri, 02 Jun 2006 23:34:08 -0700, "G.T." <[email hidden]>

Quoted message said:

Quoted message said:

Quoted message said:

Every day, I pedal back into town on a smooth, paved country road that
runs along the bluffs above the Arkansas River.

The road is about as straight and level as a bowling alley--I can see
the sole traffic light almost a mile away.

But the road dips twice as it crosses the heads of small gullies.

Each dip is roughly enough to hide a single-story house.

Assuming that I'm doing 20 mph on the flat part of the road (usually a
little over that), and assuming that I put out the same effort (maybe
I try harder?) . . .

What should happen to my overall speed?

Do I go faster, slower, or the same speed for the whole mile when I
roller-coaster through these two dips, compared to what I'd do if the
whole road was flat?

Usually, my speed rises to 25 mph by the bottom of the dip and then
reaches 27-30 mph as I start climbing the far side. (Speedometer lag?)
By the time that I climb back up to the level road again, the speed is
back down to about 20 mph again.

It seems as if the climb should cancel the drop, but the speedometer
seems to show only a rise above 20 mph and a fall back to 20 mph.

Is this just because I get excited about going faster down into the
dip, pedal harder and tuck in without realizing it, and then work even
harder climbing back up out of the dip?

That would make me feel better about conservation of energy, but it's
hard to believe that I've got an extra 5-7 mph tucked up my sleeve
every day.

Carl Fogel

Now it seems even worse.

There I am, going a steady 20 mph on the level.

If I drop into a dip, my speed rises to say 25 mph by the bottom, and
then drops back down to 20 just as I reach the top. Obviously, my
average speed is faster.

http://www.physicalgeography.net/fundamentals/6e.html

If you're going 20 mph before the dip, then you're not going 20 mph when
you leave the dip unless you put more energy into the effort of getting
out of the dip.

Quoted message said:

If I reverse the dip and turn it into a little hill, then my speed
drops to say 15 at the top of the rise, and then increases back to 20
at the bottom. Obviously, my average speed is lower.

Slightly. If you're not going faster than 20 mph at the bottom of the
hill then you were riding the brakes or scrubbing energy in some other
manner.

Quoted message said:

So dips increase my speed and little hills reduce it?

They both decrease it. But you knew that.

Greg

Dear Greg,

Er, no, I didn't. And I'm still not sure that I do.

Jobst mentioned a demo involving rolling balls, so I googled for ball
+ dip + physics.

Here's a site that seems to say that the ball rolling through the dip
goes through the dip faster and then returns to its original speed. If
so, then something sneaky is going on and going through the dip
produces a greater speed through the dip and then a return to the
original speed:

"Identical balls are launched at the same time with the same velocity
from the left front end of the two-track gizmo photographed below.
(Because this is a physics problem, there is no friction.) A race of
the balls will then ensue. The ball on the flat track clearly proceeds
across the track at a constant speed. The ball on the dipped track
goes for a while at that same speed, goes faster while it is in the
dipped part of the track, then returns to its original speed for the
final segment of the track. Note that it also travels further."

http://www.physics.umd.edu/lecdem/outreach/QOTW/arch1/q002.htm

I don't know if I'm misunderstanding the description above, if it's
mistaken, or if the powered bicycle with more wind drag effect differs
significantly form the unpowered ball with less wind drag.

But it does seem to say (and the video shows) that the ball rolling
through the dip beats hell out of the other ball and that they both
wind up on the far side at the same speed.

Here's an animated example that seems to show the same thing, though I
can't tell if the exit speeds are the same:

http://www.schulphysik.de/ntnujava/racingBall/racingBall.html

Does it seem to you that these sites are saying that going through the
dip a) gets the ball to the same point faster than a level path, and
b) produces balls going the same speed at the far end?

If so, does that seem to disagree with Jobst, who (I think) is saying
that the ball going through the dip reaches the runout first, but is
going slower at that point?

I may well be misunderstanding Jobst, so have a look at his post. The
other sites that I've looked at seem to focus on which ball "wins" the
race without saying how fast each ball is going after both pass the
dip and are on the level runout.

Cheers,

Carl Fogel

Quoted message said:

On Fri, 02 Jun 2006 23:34:08 -0700, "G.T." <[email hidden]>

Quoted message said:

Quoted message said:

On Fri, 02 Jun 2006 20:54:42 -0600, [email hidden] wrote:

>Every day, I pedal back into town on a smooth, paved country road that
>runs along the bluffs above the Arkansas River.
>
>The road is about as straight and level as a bowling alley--I can see
>the sole traffic light almost a mile away.
>
>But the road dips twice as it crosses the heads of small gullies.
>
>Each dip is roughly enough to hide a single-story house.
>
>Assuming that I'm doing 20 mph on the flat part of the road (usually a
>little over that), and assuming that I put out the same effort (maybe
>I try harder?) . . .
>
>What should happen to my overall speed?
>
>Do I go faster, slower, or the same speed for the whole mile when I
>roller-coaster through these two dips, compared to what I'd do if the
>whole road was flat?
>
>Usually, my speed rises to 25 mph by the bottom of the dip and then
>reaches 27-30 mph as I start climbing the far side. (Speedometer lag?)
>By the time that I climb back up to the level road again, the speed is
>back down to about 20 mph again.
>
>It seems as if the climb should cancel the drop, but the speedometer
>seems to show only a rise above 20 mph and a fall back to 20 mph.
>
>Is this just because I get excited about going faster down into the
>dip, pedal harder and tuck in without realizing it, and then work even
>harder climbing back up out of the dip?
>
>That would make me feel better about conservation of energy, but it's
>hard to believe that I've got an extra 5-7 mph tucked up my sleeve
>every day.
>
>Carl Fogel

Now it seems even worse.

There I am, going a steady 20 mph on the level.

If I drop into a dip, my speed rises to say 25 mph by the bottom, and
then drops back down to 20 just as I reach the top. Obviously, my
average speed is faster.

http://www.physicalgeography.net/fundamentals/6e.html

If you're going 20 mph before the dip, then you're not going 20 mph when
you leave the dip unless you put more energy into the effort of getting
out of the dip.

Quoted message said:

If I reverse the dip and turn it into a little hill, then my speed
drops to say 15 at the top of the rise, and then increases back to 20
at the bottom. Obviously, my average speed is lower.

Slightly. If you're not going faster than 20 mph at the bottom of the
hill then you were riding the brakes or scrubbing energy in some other
manner.

Quoted message said:

So dips increase my speed and little hills reduce it?

They both decrease it. But you knew that.

Greg

Dear Greg,

Er, no, I didn't. And I'm still not sure that I do.

Jobst mentioned a demo involving rolling balls, so I googled for ball
+ dip + physics.

Here's a site that seems to say that the ball rolling through the dip
goes through the dip faster and then returns to its original speed. If
so, then something sneaky is going on and going through the dip
produces a greater speed through the dip and then a return to the
original speed:

"Identical balls are launched at the same time with the same velocity
from the left front end of the two-track gizmo photographed below.
(Because this is a physics problem, there is no friction.) A race of
the balls will then ensue. The ball on the flat track clearly proceeds
across the track at a constant speed. The ball on the dipped track
goes for a while at that same speed, goes faster while it is in the
dipped part of the track, then returns to its original speed for the
final segment of the track. Note that it also travels further."

http://www.physics.umd.edu/lecdem/outreach/QOTW/arch1/q002.htm

I don't know if I'm misunderstanding the description above, if it's
mistaken, or if the powered bicycle with more wind drag effect differs
significantly form the unpowered ball with less wind drag.

Yes, they differ significantly.

Greg
--
"All my time I spent in heaven
Revelries of dance and wine
Waking to the sound of laughter
Up I'd rise and kiss the sky" - The Mekons

On Sat, 03 Jun 2006 00:19:50 -0700, "G.T." <[email hidden]>

Quoted message said:

Quoted message said:

On Fri, 02 Jun 2006 23:34:08 -0700, "G.T." <[email hidden]>

Quoted message said:

[email hidden] wrote:

>On Fri, 02 Jun 2006 20:54:42 -0600, [email hidden] wrote:
>
>
>
>>Every day, I pedal back into town on a smooth, paved country road that
>>runs along the bluffs above the Arkansas River.
>>
>>The road is about as straight and level as a bowling alley--I can see
>>the sole traffic light almost a mile away.
>>
>>But the road dips twice as it crosses the heads of small gullies.
>>
>>Each dip is roughly enough to hide a single-story house.
>>
>>Assuming that I'm doing 20 mph on the flat part of the road (usually a
>>little over that), and assuming that I put out the same effort (maybe
>>I try harder?) . . .
>>
>>What should happen to my overall speed?
>>
>>Do I go faster, slower, or the same speed for the whole mile when I
>>roller-coaster through these two dips, compared to what I'd do if the
>>whole road was flat?
>>
>>Usually, my speed rises to 25 mph by the bottom of the dip and then
>>reaches 27-30 mph as I start climbing the far side. (Speedometer lag?)
>>By the time that I climb back up to the level road again, the speed is
>>back down to about 20 mph again.
>>
>>It seems as if the climb should cancel the drop, but the speedometer
>>seems to show only a rise above 20 mph and a fall back to 20 mph.
>>
>>Is this just because I get excited about going faster down into the
>>dip, pedal harder and tuck in without realizing it, and then work even
>>harder climbing back up out of the dip?
>>
>>That would make me feel better about conservation of energy, but it's
>>hard to believe that I've got an extra 5-7 mph tucked up my sleeve
>>every day.
>>
>>Carl Fogel
>
>
>Now it seems even worse.
>
>There I am, going a steady 20 mph on the level.
>
>If I drop into a dip, my speed rises to say 25 mph by the bottom, and
>then drops back down to 20 just as I reach the top. Obviously, my
>average speed is faster.

http://www.physicalgeography.net/fundamentals/6e.html

If you're going 20 mph before the dip, then you're not going 20 mph when
you leave the dip unless you put more energy into the effort of getting
out of the dip.

>If I reverse the dip and turn it into a little hill, then my speed
>drops to say 15 at the top of the rise, and then increases back to 20
>at the bottom. Obviously, my average speed is lower.

Slightly. If you're not going faster than 20 mph at the bottom of the
hill then you were riding the brakes or scrubbing energy in some other
manner.

>So dips increase my speed and little hills reduce it?
>

They both decrease it. But you knew that.

Greg

Dear Greg,

Er, no, I didn't. And I'm still not sure that I do.

Jobst mentioned a demo involving rolling balls, so I googled for ball
+ dip + physics.

Here's a site that seems to say that the ball rolling through the dip
goes through the dip faster and then returns to its original speed. If
so, then something sneaky is going on and going through the dip
produces a greater speed through the dip and then a return to the
original speed:

"Identical balls are launched at the same time with the same velocity
from the left front end of the two-track gizmo photographed below.
(Because this is a physics problem, there is no friction.) A race of
the balls will then ensue. The ball on the flat track clearly proceeds
across the track at a constant speed. The ball on the dipped track
goes for a while at that same speed, goes faster while it is in the
dipped part of the track, then returns to its original speed for the
final segment of the track. Note that it also travels further."

http://www.physics.umd.edu/lecdem/outreach/QOTW/arch1/q002.htm

I don't know if I'm misunderstanding the description above, if it's
mistaken, or if the powered bicycle with more wind drag effect differs
significantly form the unpowered ball with less wind drag.

Yes, they differ significantly.

Greg

Dear Greg,

How?

Cheers,

Carl Fogel

Quoted message said:

This one says that the ball going through the dip returns to its
original speed, not a lower speed:

Because they assume zero friction. Bicycles experience a lot of
friction in the form of wind drag. For instance, after leveling off at
the bottom of the dip, your speed will quickly fall back to ~20 mph if
that is the amount of power you are putting out... then you have to
climb a hill, so your speed will drop substantially. Momentum doesn't
last very long on a bike...

Quoted message said:

What should happen to my overall speed?

If it didn't drop, we'd have perpetual motion available to us. You will
not regain the speed from the downhill on the up due to inefficiencies.

-paul

This argument is theoretical--it has nothing to do with friction. Carl's
original assumption was that his speed at the conclusion of the dip/hill
returns to the original value, due to conservation of energy.

Your problem is more basic than friction, wind drag, or any real-world
details. There is a difference between distance-based average and time
based average. Let's say you ride one mile up a hill 4 MPH, and then coast
back down at 30 MPH. You spend 15 minutes going up, and 2 minutes going
down. You spend half your distance at 4 MPH and half at 30. Is your
average speed 16 MPH? Your time-based average is 2 miles/17 minutes, or 7
MPH.

There is a classic puzzler based on this fallacy: Lets say you want to
travel 30 miles at an average speed of 30 MPH. You go the first 15 miles at
15 miles per hour. How fast do you have to go the rest of the way to meet
your objective. The answer is that you can't do it. You used up your whole
hour in the first half of the trip, so you would have to do the second half
in zero time.

Ron Ruff said:

Quoted message said:

This one says that the ball going through the dip returns to its
original speed, not a lower speed:

Because they assume zero friction. Bicycles experience a lot of
friction in the form of wind drag. For instance, after leveling off at
the bottom of the dip, your speed will quickly fall back to ~20 mph if
that is the amount of power you are putting out... then you have to
climb a hill, so your speed will drop substantially. Momentum doesn't
last very long on a bike...

Dear Ron,

But these dips seem to be short enough and steep enough that the
momentum does last.

I do wonder about the speedometer lag, since the high speed always
shows up about a third of the way up the far side.

I'm beginning to think that there will be a wide variation in results
for dips of different width and depth, given the same entry speed and
power.

But short of a power meter, I can't see any way to test what I'm doing
as gravity boosts my speed and cadence about 25%. I know that I pedal
faster, but I can't really say if I'm putting out more, less, or the
same power. Less seems very unlikely, while more seems to imply that
I've got a lot of extra power handy--flattering, but also unlikely.

My trusty bike-speed calculator is no help because the dips aren't
nearly long enough to reach terminal velocity:

http://www.kreuzotter.de/english/espeed.htm

With all the details plugged in (weight, height, and altitude), a mere
1.4% grade is enough to boost my 20 mph speed to over 25 mph with
steady power.

So I'm thinking that these dips may be closer to a ball demo/roller
coaster than to a situation where the much higher wind drag has time
to overpower them. Over the next few rides, I'm planning to time the
silly things and see what the distances are.

Cheers,

Carl Fogel

Leo Lichtman said:

This argument is theoretical--it has nothing to do with friction. Carl's
original assumption was that his speed at the conclusion of the dip/hill
returns to the original value, due to conservation of energy.

Your problem is more basic than friction, wind drag, or any real-world
details. There is a difference between distance-based average and time
based average. Let's say you ride one mile up a hill 4 MPH, and then coast
back down at 30 MPH. You spend 15 minutes going up, and 2 minutes going
down. You spend half your distance at 4 MPH and half at 30. Is your
average speed 16 MPH? Your time-based average is 2 miles/17 minutes, or 7
MPH.

There is a classic puzzler based on this fallacy: Lets say you want to
travel 30 miles at an average speed of 30 MPH. You go the first 15 miles at
15 miles per hour. How fast do you have to go the rest of the way to meet
your objective. The answer is that you can't do it. You used up your whole
hour in the first half of the trip, so you would have to do the second half
in zero time.

Dear Paul and Leo,

Have a look at this page and its video:

"The answer is (b); the ball on the dipped track gets to the end first
and wins the race. The two balls go along together for the first part
of the race. As the ball on the dipped track goes down, its horizontal
velocity increases, so it gets ahead. When it returns to its original
level, it slows down to its original horizontal speed, but in so doing
it never goes slower than the ball on the flat track, so it never gets
behind the other ball or even allows the flat track ball to catch up.
The two balls then move along at the same speed with the dipped track
ball remaining ahead of the straight track ball by a constant amount."

http://www.physics.umd.edu/lecdem/outreach/QOTW/arch1/a002.htm

It seems to say that going through the dip wins.

Jobst suggested this demo, so I googled for it. He seems to be either
disagreeing with the conclusion above for the balls, or else trying to
explain that the higher wind drag for a bicycle will at some point
change the outcome.

Now I'm wondering whether short and steep enough dips can lead to a
powered bicycle working more like the stupid balls (going through the
dip wins and stays ahead forever) than like what Jobst observed with
two riders and those handy side-by-side, dip-and-level paths (dip
rider reaches far side sooner than level path rider, but is going so
much slower that level rider passes him).

Cheers,

Carl Fogel

Leo Lichtman said:

This argument is theoretical--it has nothing to do with friction.

You haven't watched the rolling ball experiments, have you?

Quoted message said:

Carl's
original assumption was that his speed at the conclusion of the dip/hill
returns to the original value, due to conservation of energy.

Yes, in a frictionless world he's right, taking the dip example:

"As the ball on the dipped track goes down, its horizontal velocity
increases, so it gets ahead. When it returns to its original level, it
slows down to its original horizontal speed, but in so doing it never
goes slower than the ball on the flat track, so it never gets behind the
other ball or even allows the flat track ball to catch up. The two balls
then move along at the same speed with the dipped track ball remaining
ahead of the straight track ball by a constant amount."

Quoted message said:

Your problem is more basic than friction, wind drag, or any real-world
details.

No, watch the rolling ball experiments.

Greg
--
"All my time I spent in heaven
Revelries of dance and wine
Waking to the sound of laughter
Up I'd rise and kiss the sky" - The Mekons

On Sat, 03 Jun 2006 11:14:19 -0700, "G.T." <[email hidden]>

Quoted message said:

Leo Lichtman said:

This argument is theoretical--it has nothing to do with friction.

You haven't watched the rolling ball experiments, have you?

Quoted message said:

Carl's
original assumption was that his speed at the conclusion of the dip/hill
returns to the original value, due to conservation of energy.

Yes, in a frictionless world he's right, taking the dip example:

"As the ball on the dipped track goes down, its horizontal velocity
increases, so it gets ahead. When it returns to its original level, it
slows down to its original horizontal speed, but in so doing it never
goes slower than the ball on the flat track, so it never gets behind the
other ball or even allows the flat track ball to catch up. The two balls
then move along at the same speed with the dipped track ball remaining
ahead of the straight track ball by a constant amount."

Quoted message said:

Your problem is more basic than friction, wind drag, or any real-world
details.

No, watch the rolling ball experiments.

Greg

Dear Greg,

Regrettably, for Carl to be right, Carl would have to have a firmer
position than it all seems very fishy.

Those stupid balls show that the dip wins--same final speed, but
faster for a short section.

Others have suggested that this smacks of perpetual motion. Since it's
a physics department demo, I assume that perpetual motion has been
eliminated, but I'm hoping that no one asks me to explain exactly why.

Whether wind drag and steady pedal power alter the case enough to
change things for a bicycle with particular initial speed heading into
a dip with a particular depth or width--well, that's the question.

Jobst seems to be saying that he's seen a pair of riders, one on a dip
and the other on a parallel level path, ending up with the dip rider
ending up ahead as he exits the dip, but going noticeably more slowly
than the level rider, who probably overtakes him.

How deep and wide the dip was and how much speed and power were
involved might affect things.

How steady the power was would require a power meter.

My two dips are so short that I can't really say that my power is
steady.

My speed rises dramatically, but that seems likely to be mostly
gravity, not me unleashing my pathetic reserves.

Since my speed rises from about 20 mph to 25-27 mph and doesn't drop
below 20 mph at any point, it seems as if I'd have to be providing
enough extra power to raise my speed from about 15 mph to 20 mph over
what steady power would provide

You can see why I'm not about to claim that it's all due to my mighty
legs. (Who's going to believe that I have an extra 5 mph on the flats,
much less uphill?)

But since my cadence has to rise about 25%, I don't trust my
impression that I'm putting out the same power.

Still, I'm not clear why wind drag should slow the winner of the
ball-race down so much more than the loser. I suspect that a solution
to this would involve a lot of graphs and curves, but maybe someone
will come up with an elegant explanation.

Any explanation should also handle the reverse case, where a rider
goes over a short hill (the dip upside-down). I don't have anything
like that on my daily ride.

Maybe googling for roller-coasters will turn something up.

Cheers,

Carl Fogel