Threshold speed for stale red light

[teoman]

You would be losing more energy to drag and friction if you never stopped / slowed down for the stoplight.

For the amount of gasoline lost, i (personally) would still stick with what i found. That is a good enough approximation in my opinion.

[teoman]

Just to ponder on the question a bit further...

The unknowns were friction and air drag, these increase with speed, as you are below the set speed these will always be lower than stopped or accelerating.

Lets still assume that the guy was traveling at 40 mph.
And lets assume that he consumes 4l/100km @ 40 mph.

All of the energy in the fuel is going to combat air drag and other frictions. As the other dude mentioned if we were in space, once you accelerated to 40mph you would continue untill infinity.


Lets assume that you stopped in 200 m and re-accelerated in 300m. So total distance is 500m.

4000ml / (100.000) = 0.04 ml of fuel per meter.

We pulled 500m from a well calibrated deep dark datasource...
500m * 0.04ml/m = 20ml of fuel consumed in 500m.

If we assume that the speed was linearly decreased and linearly increased and drag and friction are linear with speed (which they are absolutely NOT, but for a slow speed of 40mph we can assume that it is without introducing an error of several orders of magnitude).

Then the total drag and friction is exactly half of that value... so 10ml of fuel.

Obviously you meed to plug in the appropriate numbers. So you wasted a total of 11ml + 10ml of fuel for the stop and go.

Had you not slowed down at all, you would have used only 20ml of fuel.

Bu you did travel at 20mph for 500m of the route and lost time.

Obviously you need proper data sources for these calculations.


(And had you traveled at 20mph all along, you would have consumed 10ml of fuel in total, so you wasted 11 ml from a general efficiency perspective, apples to apples comparison where total distance and time are equal).

[redpoint5]

Drag has nothing to do with the paradox of expending a linear amount of chemical energy, and gaining an exponential amount of kinetic energy.

Something isn't adding up correctly here. I maintain that Daox made no error in his reply.

[teoman]

That is not what i said.

Conservation of energy, it cannot dissapear, so all the fuel you are using while at steady speed is effectively going to drag and friction.

[redpoint5]

I'll post my question in a physics forum.

[JRMichler]

The energy to accelerate from zero to a speed (or decelerate to zero from a speed) is 1/2 X mass X speed^2. We start by ignoring friction, hills, driveline losses, engine inefficiency, and air drag. An ideal engine that accelerates a vehicle to a speed will burn an amount of fuel proportional to the kinetic energy.

Sample calculation:
Assume a 3000 lb vehicle.
At zero speed, the kinetic energy is zero.

At 10 MPH, the kinetic energy is 0.5 X 3000 lbs / 32.2 ft/sec^2 X (10 mi/hr X 5280 ft/mi / 3600 sec/hr)^2 = 10,020 ft-lbs kinetic energy.

At 20 MPH, the kinetic energy is 0.5 X 3000 / 32.2 X (20 X 5280 / 3600)^2 = 40,080 ft-lbs.

To accelerate from zero to 10 MPH takes 10,020 ft-lbs of energy.
To accelerate from zero to 20 MPH takes 40,080 ft-lbs of energy.
To accelerate from 10 MPH to 20 MPH takes 40,080 - 10,020 = 30,060 ft-lbs of energy.
Accelerating from 10 to 20 takes three times as much energy as accelerating from 0 to 10.

[freebeard]

Originally Posted by redpoint5

Still doesn't explain the constant rate of acceleration due to gravity. Gravity can't input more force, and yet you fall at the same rate of acceleration.

I'd let that go as a talking point.

stefanv does a good job with the Newtonian physics, but consider: https://en.wikipedia.org/wiki/Potential_energy

Gravity is poorly understood, it is a side effect of the electric nature of the universe, like the Casimir effect.

Back ontopic, I like shooting past cars immobilized at the light as much as anyone, but just after I got my Superbeetle, I slowed for a red light and a black Jetta behind me sped up, raced past me, pulled back into my lane, realized the light was red, jammed the brakes, went hammer down when it turned green, and then realized I was right on his tail and he brake-checked me. Like I was invading his personal space.

I hit him square, so the hood was damaged but not the headlights. He pulled over but when I asked about his insurance he remembered he had somewhere to be.

Grrr

[redpoint5]

Originally Posted by JRMichler

The energy to accelerate from zero to a speed (or decelerate to zero from a speed) is 1/2 X mass X speed^2. ...

Accelerating from 10 to 20 takes three times as much energy as accelerating from 0 to 10.

I have no problem understanding the math, but rather the paradox that reality shows us.

A rocket in space with a constant weight and thrust will accelerate at a linear rate. Somehow it gains kinetic energy exponentially, but expends energy linearly.

From experience, I can tell you it doesn't take 3x as long to accelerate from 10-20 MPH as it does from 0-10 MPH. This suggests it doesn't take 3x the energy.

Originally Posted by freebeard

I hit him square, so the hood was damaged but not the headlights. He pulled over but when I asked about his insurance he remembered he had somewhere to be.

Perhaps there is a correlation between people who don't plan ahead when approaching red lights, and people who don't plan ahead to get insurance.

It's too bad you didn't have a cattle guard on that Beetle. Maybe he would have learned the lesson then.

[JRMichler]

If you accelerate a land vehicle at constant acceleration, it will take the same time to accelerate from 0 to 10 as from 10 to 20. But the acceleration from 10 to 20 will take three times the distance as the acceleration from 0 to 10. Same force times triple the distance equals three times the energy.

A wheel driven land vehicle generates force by pushing against a (relatively) infinite mass, the Earth. A rocket is different. It generates force by throwing mass in the opposite direction at high velocity. A properly geared wheel driven land vehicle can generate large force at near zero speed using very little power. A rocket uses huge power to generate force at low speed, so has extremely low efficiency.

[freebeard]

I have no problem understanding the math, but rather the paradox that reality shows us.

Reality doesn't show us paradoxes. Those are all in [y]our head[s].

Wheels vs rockets is beside the point. In a gravitational gradient you're trading potential for kinetic energy.