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Hypermiling techniques?

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If X is the distance traveled, then Y is the Force. Both fast and slow acceleration are boxes, neither is sloped as fast acceleration means a horizontal line with greater Y than slower acceleration, but both are flat. The formula for distance is s=V^2/(2a), so to get to a particular velocity, the distance to get there will be less if the acceleration is faster so the box is shorter in X for faster acceleration to get to a given speed and the areas are the same. If you substitute that into E=F*s you get the original formula with the a term cancelled out.

This got me thinking about how to accelerate in terms of distance traveled since we generally travel for a distance, not for a time. Assuming that there's a need to get to a higher speed, such as an entrance ramp onto a highway, there's a maximum distance available for the acceleration, in this case the merge lane. Ignoring for the moment the higher heat losses the the drive train, I think the most energy efficient way to acceleration would be to go at the minimum safe speed until you're just at the minimum distance from the merge lane end you'll require to get up to highway speed and then floor it. That way you travel at the slowest safe speed the longest distance but still are at highway speed when you finally do the merge.

If you accelerate at a constant rate to just get to highway speed at the end of the merge lane, you'll spend more time at higher speed. OTOH if you accelerate hard at the start then go at highway speed the remaining distance to the end of the merge lane you'll travel longer at higher speed in the merge lane where lower speed is safe.

The actual best rate of acceleration at the end of the merge lane is very likely less than maximum because of high current heating losses, but we'd need a lot more data to know what the trade off between heat loss and drag loss is.

X=distance, Y=speed, Area under the curve is the energy used. Assuming you start and end at Y=0, and you reach some maximum Y over distance X, the slower you accelerate (and decelerate) the more the area approaches a triangle. The faster you accelerate, the more the area approaches a rectangle. A rectangle has more area than a triangle for a given X and Y. This is why slow acceleration and deceleration works, and it's also why short trips are less efficient than long trips--assuming you can keep a more-or-less constant speed once you get up to speed, as the distance covered during the slope of acceleration and deceleration is small in comparison to the distance travelled.
 
X=distance, Y=speed, Area under the curve is the energy used. Assuming you start and end at Y=0, and you reach some maximum Y over distance X, the slower you accelerate (and decelerate) the more the area approaches a triangle. The faster you accelerate, the more the area approaches a rectangle. A rectangle has more area than a triangle for a given X and Y. This is why slow acceleration and deceleration works, and it's also why short trips are less efficient than long trips--assuming you can keep a more-or-less constant speed once you get up to speed, as the distance covered during the slope of acceleration and deceleration is small in comparison to the distance travelled.
But distance times speed doesn't equal energy. Force times distance equals energy.

If distance times speed equaled energy then moving a light object would take the same energy as moving a heavy object so if a humming bird flew the same route exactly matching the speed of an 18 wheeler they would both use the same energy. Obviously that's not true.

It would also mean that the Voyager spacecraft, which moves at a nearly constant speed, would require a huge energy input since it's distance is immense and is always increasing.
 
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But distance times speed doesn't equal energy. Force times distance equals energy.

If distance times speed equaled energy then moving a light object would take the same energy as moving a heavy object so if a humming bird flew the same route exactly matching the speed of an 18 wheeler they would both use the same energy. Obviously that's not true.

It would also mean that the Voyager spacecraft, which moves at a nearly constant speed, would require a huge energy input since it's distance is immense and is always increasing.

That's right:

Force times distance = Energy
and​
Force times speed = Power

Because aerodynamic drag (Force) increases as the square of speed, the aerodynamic portion of energy consumed to go a given distance (Wh/mi) goes up as the square of speed, and the aerodynamic portion of the power needed to go that speed (W) goes up as the cube of speed.

Power (W) and energy (Wh) get confused all the time...
 
and therefore what? assuming relatively low (<70mph) speeds (and therefore trivial aero and rolling resistance drag) nothing is different from your high school physics lesson.

the main point is that coasting (not adding acceleration, and not braking (with either regen braking or friction braking) is the most energy efficient way to travel.

An intuition pump to illustrate this is:

imagine you are at the top of a gentle slope (so that aero and rolling resistance drag is trivial for purposes of this hypo) with a totally empty battery. Way off in the distance, there is a supercharger station. What method will bring you closer to the super charger?

Case 1: only coasting in neutral as efficiently as possible (no regen or friction braking).

Case 2: slowing car with regen braking to charge the battery, trading kinetic energy (decreasing speed from the regen braking) for potential energy (adding to the battery charge). When you lose speed from the hill, you then use the battery.

The only situation in which Case 2 would be better is if you add back in the aero drag and the hill was so steep that you gained so much speed (> 70? > 100?) that you lost more to aero drag then you would lose to regen inefficiency. In all other (more typical) cases, Case 1 with only coasting would get you closer to the supercharger (i.e., convert more of your potential energy into moving your cars mass towards the supercharger than Case 2 using regen.

putting time on the x axis instead might illustrate it better to show the area of the graph is the distance covered:

18672_Speed-Time%20Curves.JPG


adding some regen braking will allow some additional upward accel as the battery is then recharged, but because of the inherent regen inefficiencies, the downward slope of the braking line will always be steeper than the resulting upward slope of the accel line so you are losing total distance by using regen.
 
It is probably also the case the the minimum energy speed is slightly higher in very hot or very cold weather as the constant non-motor power is higher.

Also, does anyone know whether it's better to use the A/C or open the windows on a mildly hot day?
FWIW, my recent experience driving in ~60-65F weather, opening the sunroof to the vent setting and turning off climate control was very comfortable and efficient.
 
Just look at it this way... whenever you use regen you are wasting about 20% of the range you are recapturing to efficiency losses. When you coast, there are no efficiency losses because you are not converting that forward momentum into electricity to be stored in your battery. What you waste in regen losses translates directly to greater distance traveled while coasting. If you remember this, you will find yourself coasting more than using regen in almost every situation. Whenever you use regen, one out of every five feet is wasted and you stop sooner. Not so when coasting.
 
Whenever you use regen, one out of every five feet is wasted and you stop sooner. Not so when coasting.

But regen is analogue, rather than binary. You don't always have your foot totally off the accelerator pedal when using regen. Keeping the power meter close to zero amounts to the same thing without the problems associated with coasting (assuming that by coasting you mean coasting in neutral). It's certainly true that the longer you take to accelerate or come to a stop the lower your power usage will be.
 
But regen is analogue, rather than binary. You don't always have your foot totally off the accelerator pedal when using regen. Keeping the power meter close to zero amounts to the same thing without the problems associated with coasting (assuming that by coasting you mean coasting in neutral). It's certainly true that the longer you take to accelerate or come to a stop the lower your power usage will be.

By coasting I meant modulating the pedal so there is no regen or power input.
 
It is probably also the case the the minimum energy speed is slightly higher in very hot or very cold weather as the constant non-motor power is higher.

Also, does anyone know whether it's better to use the A/C or open the windows on a mildly hot day?

Keep the windows closed and use the climate control: opening windows ruins the car's aerodynamics (notice how much louder it gets from the wind noise and buffeting when you open windows? that's energy lost to the atmosphere).

I believe that's actually Tesla's recommendation, too, though I don't remember where I read it.

- - - Updated - - -

Case 2: slowing car with regen braking to charge the battery, trading kinetic energy (decreasing speed from the regen braking) for potential energy (adding to the battery charge). When you lose speed from the hill, you then use the battery.

The only situation in which Case 2 would be better is if you add back in the aero drag and the hill was so steep that you gained so much speed (> 70? > 100?) that you lost more to aero drag then you would lose to regen inefficiency. In all other (more typical) cases, Case 1 with only coasting would get you closer to the supercharger (i.e., convert more of your potential energy into moving your cars mass towards the supercharger than Case 2 using regen.

There are a lot of big hills in Colorado where your Case 2 is by far the more efficient: I can add six miles of Rated range to the battery, using regen to hold a constant 60 mph, when descending from the summit of some of the passes here. You can't ignore aero drag: even at 55 mph it represents a huge portion of the car's energy usage. If the hill is long enough and steep enough, Case 2 wins every time.

And allow me this nit: I'm not converting kinetic energy to potential energy coming down off the pass: I'm converting potential energy (by giving up altitude while holding a constant speed, so kinetic energy is constant) to chemical energy stored in the battery.
 
There are a lot of big hills in Colorado where your Case 2 is by far the more efficient: I can add six miles of Rated range to the battery, using regen to hold a constant 60 mph, when descending from the summit of some of the passes here. You can't ignore aero drag: even at 55 mph it represents a huge portion of the car's energy usage. If the hill is long enough and steep enough, Case 2 wins every time.

And allow me this nit: I'm not converting kinetic energy to potential energy coming down off the pass: I'm converting potential energy (by giving up altitude while holding a constant speed, so kinetic energy is constant) to chemical energy stored in the battery.

Hear, hear, Stevezzzz!

I will give a specific example. I-70 West from the west entrance of Eisenhower Tunnel to the Silverthorne exit for the supercharger. If I descend using regen at 60-65 mph, then I take the turn at the bottom of the exit with 6 more rated miles in the battery. If I descend coasting, it will be at 90+ mph, terminal velocity pouring that kinetic energy into overcoming aerodynamic drag. Even if I could slow down with regen at the exit, the extra kinetic energy between 60 and 90 would be less than a rated mile.

Where coasting wins over regen is on small rolling hills with total altitude differences under 100 meters, 328 feet.
 
Just look at it this way... whenever you use regen you are wasting about 20% of the range you are recapturing to efficiency losses.

You are correct that regenerative braking is not 100% efficient. But getting 80% back is better than getting nothing back. How efficient regen is, makes no difference. It is always better than nothing. I think what you mean is that not needing regen nor brakes to slow down the car, but rather let it coast to the point where it stops, is the best use of energy. It certainly is! You accelerate just enough that when you let it coast, it will come to a stop at your destination. Of course this would mean you are going much slower than driving at normal speed and then using regen to stop at your destination. And that's where it comes down to the same thing again. Going slower is more efficient. By letting it coast to a stop, you are not more efficient because you avoided regen, you are more efficient because you drove slower overall.

The reason I'm pointing this out is because many people tend to believe that because regen is not 100% efficient it should be avoided. It is the wrong thing to take away from this. Regen is the one thing that makes EV so efficient. There is almost no time and place in normal driving situations for coasting (be it feathering the pedal or actually putting it in N). In normal driving, the flow of traffic expects you to keep a speed until you read a point where you have to slow down. You would annoy the heck out of everyone if you started coasting 1 mile before the exit of a freeway to reach 25 mph when you exit.

I see people here avoid regen thinking it would be wasteful. It is the opposite. It is a very useful tool for driving efficient in traffic.
 
getting 80% back is better than getting nothing back. How efficient regen is, makes no difference. It is always better than nothing.

people tend to believe that because regen is not 100% efficient it should be avoided. It is the wrong thing to take away from this. Regen is the one thing that makes EV so efficient. . . . You would annoy the heck out of everyone if you started coasting 1 mile before the exit of a freeway to reach 25 mph when you exit.

I see people here avoid regen thinking it would be wasteful. It is the opposite. It is a very useful tool for driving efficient in traffic.

This thread is about hypermiling -- driving as energy efficiently as possible.

Using regen is always less energy efficient than just coasting to the same end point unless you use regen to avoid a high speed induced by a long steep hill descent.

When you lose speed you go less distance until you need to use power again to add back speed. If you can coast, without using regen to exactly that stop sign, or stop light, or your driveway or the supercharger, then you will have achieved that distance without having to add any more power.

If you think regen is better, and then apply regen and thus slow down and are not able to coast to your end point, you then have to add more power from the battery that you just recharged. But ! oops! the battery power that you need to reach the end point, exceeds the battery power that you added from the regen. because regen always results in some energy loss.
 
...Where coasting wins over regen is on small rolling hills with total altitude differences under 100 meters, 328 feet.

I would think it's speed not the height of the hill that matters. For any particular car (e.g. Model S) there should be a downhill coasting speed at which it is more efficient to use regen to avoid going any faster. It would be tedious to determine this empirically. Does anyone have enough information to do it analytically? Or perhaps Tesla has already done it?

(The tedious empirical method would be to find a steep hill and coast down, marking the stop where you stop. Then go down again using a little regen to hold the speed down a bit and a little power at the bottom until the battery reaches the same SOC as it had at the top (difficult to determine accurately!). Repeat at slightly lower speeds... )
 
I would think it's speed not the height of the hill that matters. For any particular car (e.g. Model S) there should be a downhill coasting speed at which it is more efficient to use regen to avoid going any faster. It would be tedious to determine this empirically. Does anyone have enough information to do it analytically? Or perhaps Tesla has already done it?

(The tedious empirical method would be to find a steep hill and coast down, marking the stop where you stop. Then go down again using a little regen to hold the speed down a bit and a little power at the bottom until the battery reaches the same SOC as it had at the top (difficult to determine accurately!). Repeat at slightly lower speeds... )


exactly. This interesting thread Toyota Rav4 EV Forum View topic - Regen B vs Coasting

points out that aero drag is proportional to the square of velocity. so at some point it can get quite large v quickly. I would guess that it is around 50-70 based on absolutely nothing but years of playing around and coasting in neutral in hybrids to hyper mile and noticing how quickly aero drag decels the car at various speeds.
 
This thread is about hypermiling -- driving as energy efficiently as possible.

Using regen is always less energy efficient than just coasting to the same end point unless you use regen to avoid a high speed induced by a long steep hill descent.

I totally understand and agree, but to be technical the best hypermiling technique is to go 25 mph constant. Coasting down to 0 and then accelerating up again is less efficient. So it's best to accelerate to 25 and then run all red lights LOL

Hypermiling isn't about all or nothing. We use our cars in every day traffic and within the constraints of that we can find the best method of using the energy. Regen is a brilliant way to get a lot of energy back that would otherwise be wasted. When it can be avoided by coasting, yes it's better to do that. But there is rarely a situation where you have time and space to let the car coast to a stop. If you have it, go for it.
 
Basically
1. Drive as slow as possible
2. To stop, coasting is the best option (keeping the power meter at 0)
3. If coasting is too slow/dangerous in your situation and you need to stop, regen is better than brakes.

4. Accelerate as slowly as possible.
5. Reduce speed when going uphill.
 
The next time I descend from the Eisenhower tunnel to Silverthorne SpC I'm going to try an experiment. Over several trips, allowing cruise control to hold 60-65 mph down the long, steep grade using regen, I have reliably added about 2kWh and six Rated miles to the battery. Cottonwood has driven the route even more frequently than I: his experience is consistent with mine. I hypothesize that if I join the trucks in the right lane driving, say, 35mph while using regen to hold speed, I should see a significant increase in the energy I put back into the battery, due almost entirely to reduced aerodynamic losses. I may get a chance to try it this week; will report back.