Physics of dips

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

On Fri, 02 Jun 2006 20:54:42 -0600, 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.

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

On Fri, 02 Jun 2006 22:27:17 -0600, wrote:

On Fri, 02 Jun 2006 20:54:42 -0600, 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.

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

On Fri, 02 Jun 2006 23:08:12 -0600, wrote:

On Fri, 02 Jun 2006 22:27:17 -0600, wrote:

On Fri, 02 Jun 2006 20:54:42 -0600, 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.

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 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

On 03 Jun 2006 05:24:51 GMT, wrote:

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

On Sat, 03 Jun 2006 00:08:45 -0600, wrote:

On 03 Jun 2006 05:24:51 GMT, wrote:

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/r...acingBall.html

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

CF

wrote:

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

wrote:
On Fri, 02 Jun 2006 20:54:42 -0600, 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
--
"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 00:14:19 -0600, wrote:

On Sat, 03 Jun 2006 00:08:45 -0600, wrote:

On 03 Jun 2006 05:24:51 GMT, wrote:

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/r...acingBall.html

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

CF

And some mo

http://www.physics.umd.edu/lecdem/se...osc2/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...Koch/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/ou...arch1/q002.htm

CF