Total Trip Time Optimization Formula?

smorgasbord · Jul 11, 2011

I just took my first trip beyond the range of the Roadster - 195 miles at mostly freeway speeds. Recharging was a drag. While I put more juice in enroute than I needed, this was my first long trip and I wanted to be safe, not sorry.

It occurs to me that if I had driven more slowly, I might have been able to make that trip without stopping to recharge. Would that have been faster if I'm measuring door to door time?

While I could (and did) drive at a rate of 2 miles in 105 seconds (about 70MPH), the 70amp HPC stations took 210 seconds to put those 2 miles back into the battery. That means once I depleted my mileage store (about 170 miles for my 305 Wh/mile consumption rate) I was effectively traveling at 23 MPH.

So, I get 130 miles (leaving 40 for cushion) at 70MPH and then I had another 65 miles at 34.3 MPH. I'll look at my logs tonight, but roughly speaking the total time for the 195 mile trip should have been about: 130/70 + 65/23 = 4 hours 40 minutes for an average effective speed of only 42 MPH. Now, if I had driven at 50 MPH instead could I have made the trip without stopping, and also have arrived sooner?

I know Tesla has a chart of Wh/mile on one of their web site blogs. Before I attempt it, has anyone else tried to put together a "minimum time" equation for long distance trips that nominally require charging enroute?

Doug_G · Jul 11, 2011

Yes, you can absolutely go farther by driving more slowly. In theory you can go over 400 miles on a single charge if you're willing to drive all day. Of course that is not practical in most situations; you can't drive 30 kph on a 100 kph highway. But if you can switch from a 100 kph highway to an 80 kph highway and as a result get there on a single charge, then you'll definitely be much faster.

From personal experience, Tesla's published performance curves are quite accurate, if not slightly conservative. So you can do all kinds of spreadsheet calculations based on that data. For my recent (first ever) Tesla road trip I worked up such a spreadsheet. I could dial in a speed and get a predicted Wh/km and range, and could estimate remaining SOC (and corresponding remaining range) upon arrival. That allowed me to plan my total trip including speed, charge time, etc. I decided on what speed I would drive on each leg, with the caveat that I'd watch the Wh/km and make sure it was under a certain number.

During the trip I found that the performance matched the predictions. As a result I had zero "range anxiety". I arrived with exactly my planned margin, less an extra 5 km that resulted from the GPS map being wrong! (Exit here??? What exit?!?) That's why you have margin!

What about optimizing trip time when you have to charge? That's a bit complex, in that your chargers are never in the ideal location, you probably don't need 100% top-up at every location, and you probably can't drive at your ideal speed.

As an example, for my recent Ottawa - Toronto trip I had to charge on NEMA 14-50 at a campground near Ganonoque, which really is too close to Ottawa and too far from Toronto. With a top-up to a full range mode charge in Ganonoque, the duration of the second leg was entirely determined by how fast I could drive without running out of power prematurely. So I really didn't have much control over that; I picked the speed that gave me a reasonable margin and that determined how long it took. As it happened this was 103 kph, although in reality I was able to go a little faster by drafting behind trucks (tip: trucks here have speed limiters; it appears that inter-city buses don't...).

I could however optimize the first leg. It turned out changing my speed would have a modest effect on trip time, unless I drove well over the speed limit. If I drove faster I arrived in Ganonoque with less charge, resulting in a longer trip overall. I estimated the ideal speed at 81 kph; any less or more than that the trip got longer. Driving at the speed limit of 100 kph made the trip only 7 minutes longer. In this situation driving slower is not safer; best to keep up with the traffic. Having everyone come up your ass is not worth saving 7 minutes!

But what if I drove faster? If a cop sees you at 130 kph you'll get pulled over, but they seem to usually ignore people under 120 kph. I calculated that 120 kph would make the trip a half an hour longer. So it was definitely not worth speeding!

In the end I decided to drive mostly at 105 kph. At that speed the transport trucks aren't passing you. Well most of them at least; evidently the speed limiters have a tolerance range.

Of course my wife pointed out the irony of having this fast sports car and having to drive at the speed limit...

One last thing. I found that the Estimated Miles (km) display is pretty damned accurate, as long as you give it 50 km (30 miles) to fully adapt to your current driving conditions. Just look at the distance remaining on your GPS, compare to the Estimated Miles display, and you immediately know if you're going to make it. If it looks tight then slow down!

benji4 · Jul 11, 2011

smorgasbord said:
I just took my first trip beyond the range of the Roadster - 195 miles at mostly freeway speeds. Recharging was a drag.

Nothing wrong with charging in range mode before such a trip. I've done a couple 200 mile trips now after a range mode charge with no problem at all. Even with a standard mode charge you could make it if you drive about 60mph though.... Slowing down 10mph is only going to cost you 30 min. for your whole trip and should get your pretty close to ideal range. So with a standard mode charge you'd need to switch to range mode just at the end but you'd still have 20 miles of charge left. With a range mode charge you'd have at least 40 miles left at the end.

efxjim · Jul 11, 2011

When I frequented the Aptera forum site. There was a member who wrote a great program that is still accessible on the web. It's default car is the Tesla. It uses google earth data to keep track of the elevation. You can also put in the speed you wish to travel. It generates very accurate range estimates. It is a fun toy to play with. It does take a little time to load. It was written by Karen Rei Pease.

Eberhard · Jul 11, 2011

my longest trip on a single charge was more then 260mils (420km) because i tried to do it for an 32A charger instead of an 16A charger (but was good to know they were there) i was always driving on the truck lane, never passing except uphill when they got really slow. driving very steady with cruise control. in Europe the trucks have speed llmiters at 88km/h.

Jaff · Jul 14, 2011

My longest trip was to the cottage (244 kms)...I charged in range mode (390 km range in the "tank") & rarely exceeded the speed limit by more than 5 kph.

I arrived at the cottage with 161 kms to spare.

I agree completely...if you drive at the speed limit, the estimated range of the Roadster is very accurate...might be a bit misleading if you were driving into a huge, one way increase in elevation though...the cottage is a mere 300 ft above sea level higher than my house.

Hardest part is not dispatching those drivers who deserve it during the drive...:biggrin:

Doug_G · Jul 14, 2011

Jaff said:
I arrived at the cottage with 161 kms to spare.
...
Hardest part is not dispatching those drivers who deserve it during the drive...:biggrin:

With that kind of reserve I wouldn't normally be worrying about electrons!

Of course the problem comes in with the return trip. I'm guessing you're limited to 110V charging at the cottage. I had that problem in spades on my last road trip. There's power pretty much anywhere that'll get you home in a pinch, but quite often it's the sort that takes two days to fill it up.

Jaff · Jul 18, 2011

Yep, 110V is urrently all I can get...working on my Dad to install a NEMA 14-50 with a 50 amp breaker though...:wink:

daxz · Nov 18, 2011

I created a spread sheet which will calculate this.

Extrapolating a best fit formula:
mph = 15.294 * ln( chargeRateInkW ) + 18.812
62mph = 15.294 * ln( 16.7kW) + 18.812 ~= 260Wh/mile
Charging at 16.7kW yields and ideal speed of 62mph (260 Wh/mile) for long trips. *
Numbers here are with ideal terrain/weather, it also assumes it takes about 10 minutes to get on/off highway and hook up to power and negligible wattage usage and on the road charges are up to 80% full charge.

I created this to investigate Model S packs sizes and the new super charger. Assuming the same Wh/mile curve for Model S.
Minimum of around 35kW charging is needed to maintain 75mph (303Wh/mile) speed for long distances.
Charging with 90kW chargers should be able to maintain an even pace with an ICE car which stops for 60 minutes every 250/miles when both are traveling at 75mph. Just need those chargers in the right places for my normal trips. :biggrin:

The interesting thing is that it doesn't matter much how large the pack is, just how many and how large the chargers are in route (for Tesla size packs).
A 500 mile trip takes a minimum of:
2 stops for 300 Mile pack
3 stops for 240 Mile pack
5 stops for 160 Mile pack

Eberhard · Nov 21, 2011

you have to take into your calculation, that you will start with a full charged EES and you will only need to charge to make it to the destiny. As faster you go, as longer will you have to recharge. The 500miles with the 300miles pack can you do with one stop only.

daxz · Nov 21, 2011

Eberhard said:
you have to take into your calculation, that you will start with a full charged EES and you will only need to charge to make it to the destiny. As faster you go, as longer will you have to recharge. The 500miles with the 300miles pack can you do with one stop only.

Yes, I made many assumptions
1. started with full range mode charge
2. on the road it would only be charged to 80% capacity ( 210m to first stop , 170m next stops at 76mph)
3. trip would try to minimize total travel time and only charging what is needed
4. Same size chargers (90kW) would be accessible most of route
5. stay around speed of normal traffic flow (75mph)

So if traveling 500 miles with 90kW chargers in route with 300m pack would take:
@60mph = 9.1h (0.7h charging with [1] stops )= average of 54mph
@76mph = 8h (1.4h charging with [2] stops)= average of 62mph
@80mph = 7.8h (1.5h charging with [2] stops)=average of 64mph
@84mph = 7.8h (1.7h charging [3] stops )= average of 63mph

so with super chargers (90kW) - the optimal speed is the safe speed <= ~84mph ( 135 km/h ) for large distances

Eberhard · Nov 23, 2011

you idealized the calculation a little bit. You have to leave the highway and go to the station, plus going back. This will need another 15min. better calculate 1h per stop. If you don't want do stress the EES to much, you will do charging in standard mode only.

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Total Trip Time Optimization Formula?

smorgasbord

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Doug_G

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benji4

Roadster 2.5 #0476

efxjim

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Eberhard

#421 Model S #S32

Jaff

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Doug_G

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Jaff

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daxz

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Eberhard

#421 Model S #S32

daxz

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Eberhard

#421 Model S #S32

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