# Tesla Model 3 Battery Has Power To Spare – Ludicrous Mode Anyone?

JUN 27 2018 BY GEORGE BOWER 50

The Tesla Model 3 “P” version has 500 HP available at the battery but uses only 95% of it – we do the math

Even without Ludicrous Mode the P AWD Model 3 is already quicker than BMW’s M3.

Our calculations show that the P AWD version of the Model 3 requires 471 hp out of the battery and into the drive unit. Based on Electrek hacked number the battery is good for 500 hp so we have 5% margin. Leaving room for additional performance.

As we discussed in “Has Tesla changed how it controls the front and rear motors in Model 3” the computer model has a cruise gear ratio in the back and an acceleration gear ratio in the front, which is opposite of the Model S. The primary reason being that the Tesla rear motor is now a permanent magnet motor, which is more efficient than an induction motor. It seems logical to use the more efficient motor as the cruise motor. See the bottom of the above slide for the gear ratio’s we ended up with. Our models also predict the same range for all three versions of Model 3- matching spec.

Detailed discussion of our math analysis

We have modeled quite a number of different EVs by now starting with the Tesla truck, Tesla gen 2 Roadster, BoltEV, Porsche Mission e, and Model S P100D. One thing we have learned is that the battery is the driver when it comes to estimating a vehicle’s performance. The problem is, when these EV manufacturers mention how much power a certain vehicle has, they don’t always quote the same number. Sometimes they will throw out some big number that the motor is good for, sometimes not, but more times than not the battery ends up being the pinch point. We saw that in our analysis of the Tesla Roadster. It’s usually a power limitation of the battery pack that drives the performance numbers.

We were trained from the ICE days to look at power out of the engine, so it’s just natural to think of EVs in terms of output from the electric motor (drive unit). We must retrain ourselves to think in terms of battery power, not motor power.

Here’s our estimate of the drive unit outputs for the Model 3. We estimate that the total drive unit output power delivered to the wheels of Model 3 “P” AWD at 410 hp. Next down the ladder the AWD “non-P” is estimated at 330 hp, the RWD model now shipping to customers at 271 hp and the SR RWD at 220 hp.

Of course, torque is where it’s at for EV’s. That is where we get the advantage over an ICE. An EV has torque all the way to zero RPM, an ICE does not.

Coming off the line is where the ICE has trouble, then it needs to shift which slows it down even further. In the Car and Driver article on the BMW M3, the driver could not get below a 4-second 0-60-time, even though it is rated at 3.7 seconds (versus 3.5 for Model 3 “P” AWD).

Of course, we used motor maps in our analysis.  We’ve included the motor maps for the “P” AWD Model 3. Notice there are 2 break points in the power torque curves. Breakpoint 1 is where we transition from constant torque to constant power. Breakpoint 2 we transition from constant power. We let the power fall off at a specified rate.

Of course, there’s more than just motor maps. There’s a fairly extensive list of constants that need to be input as well.

Here’s an example input sheet:

Even after all this, it is still just a computer model and it has its limitations. There’s always room for improvements and, as time goes by, more and more improvements get added.

Keith Ritter (HVACman) must take most of the credit for writing this spreadsheet. Keith knows the motors while I am more in the battery department. We volunteer all our time.

We are working on a math model of the Model 3 battery’s heat transfer performance. It’s right up Keith’s alley since he is a licensed HVAC engineer and owns his own business in Redding California- ME Systems. We hope to have some interesting comparisons of Tesla’s cooling methods versus the flat plate cooling method used by GM and the German manufacturers. Thanks for reading our articles. Stay tuned.

George and Keith

Categories: Battery Tech, Tesla

50 Comments on "Tesla Model 3 Battery Has Power To Spare – Ludicrous Mode Anyone?"

Yea could be, but 5% off would actually be way within tolerance. Also, did you add the extra weight of the front motor, gear, diff and general strengthening? If you add, say 215lb, then I guess you get to 100%. And going from a P85 to a P85D was about 280 pounds, says wikipedia.

So I guess you just have a really good model, you just don’t have all the information needed, yet.

We included an extra 200 lb for the AWD simulations to allow for front motor/suspension upgrade. We also included the weight of a “typical” driver in all simulation runs.

The hacker you quoted actually says elsewhere that the battery has a max output of 482kW or 646hp. You can see a compilation of his comments with reference links in the comments of the article you linked.

Shaun – Thanks for the tip about the hacker’s comments – we will dig further into the comment threads to see if we can find that same information and confirm the validity. That said, my copy of the hack’ed BMS screenshot under “Limits” lists “370 max discharge kW”, “1200 max discharge amps” and “402 max bus volts”. It is likely the hacker (I think it was Ingineerix) took the liberty of “calc’ing” a theoretical absolute peak kW assuming that the BMS would allow “max amps” (1200) to flow in a “max voltage” (402) condition, which would calc’s out to exactly 482 kW. But I suspect the BMS power management doesn’t work that way. It probably defines an allowable operating envelope with multiple constraints and likely would never allow the pack to exceed any of the three max limits. For example, we know a cell’s internal resistance typically drops as the cell’s state of charge (SOC) drops, which would safely allow more amps to flow in or out. That is one reason that at lower SOC’s, the BMS allows the battery to start charging at a higher amp rate, then tapers the amps as the SOC increases. So also would discharge… Read more »

Thanks for the reply HVACman. I agree that the Model 3 would likely have to be in optimal conditions and probably precondition the battery to get those full numbers, much like the Ludicrous S/X do. 1,200 amps seems perfectly reasonable from this pack when you compare it to the max amps of an S pack, relative to the difference in total pack size. I would be very surprised if the new 2170 cells couldn’t match the C-rate of the old 18650 cells, especially since I don’t recall the discharge rate of those cells being very impressive to begin with.

The way I’m starting to look at it, is the power density being asked for: @75KWh, 482KW implies a C-rate of 6.4X. Reasonable, when you consider Tesla goes for energy density as others push >10X power-density (reportedly 12X, for VW Pikes Peak). Also reasonable, that as with the Roadster, Tesla does it with extra KWh, not the more limited C-rate of NCA- lithium. Where the VW ID R was reportedly 43KWh, the AWD Performance 3 will be 75KWh. Of course, it won’t be 2,400 pounds, but if it tips in at under 4,000 it will only be several hundred more than BMW M3 and right on top, or even below many current German “sports” cars. Add low cg, throttle response and AWD digital torque vectoring, new price of 63k = game over.

Buying a Model 3 isn’t about “clean”, “safe”, “OTA”. As important (and easy to find) these things become, it’s ^THIS^.

Looking at the BMW M3, I wonder if it has the aerodynamics to keep it safely planted on the ground at 174 MPH. I do notice that they’ve lowered the profile of the front grill, but that looks about it.

There is a lot of invisible aerodynamics going on in modern parts, tiny boot spoilers alone have massive effects on some cars. Besides it’s a German car, they need to make sure it’s good at these speeds, because they will be driven on the Autobahn

xm – note the low air intakes at the front left/right lower corners of the BMW M3 and a couple of low vents at the rear lower left/right corners (outboard of the 4 engine exhausts pipes). Those likely are “diffusers” that help create a partial vacuum under the vehicle at higher speeds, which creates more downward pressure. You’ll see this concept on numerous high-performance vehicles. The Tesla next-gen Roadster has a pretty massive diffuser setup for the same reason. At 250 mph, you need some serious ground-sticking-power!

A Gordon

Personal experience: Found that the BMW M3 was very skittish at Vmax, so it is aerodynamically lacking there, perhaps due to its sedan shape. A Porsche Cayman S by comparison is pretty rock solid at nearly 180.

FYI AWD price is now 3k. 1k cheaper.

It was \$5k, now \$4k.

now \$4k, used to be 5k. Bigger steal is the performance version!!! So happy I am going to get one!

(⌐■_■) Trollnonymous

No thanks, I’ll take “Chill” mode.

Can we please do kW instead of this archaic ‘hp’ which is was invented about 2 technology generations ago?

Or will we start saying that the latest CCS standard charges your car at 469 hp?

Arne-ni – point well- taken.

but you got to realize – we’re a couple of unpaid old-school slide-rule-trained engineers still trying to drag ourselves out of the stone age and into the 21st century. As soon as we find the IP-to-SI conversion setting on our slip stick we’ll post both values:)

All kidding aside, I’m setting up my new thermal simulation model to calculate and create values in both metric and IP units, but realize it takes a whole lot longer to set up and to write dual-units – it isn’t just kW. To be rigorous, we also have to go to newtons, kg, meters, deg. Celsius, etc.

Keith

The sooner we all start speaking the same language, the easier it will be to understand each other. The rest of the world works in SI units. The medical and aerospace industries in the US work in SI units. When will the rest of the US get on board? EVs would be a good place to start, or else we fall down the rabbit hole of stupidities like the e-gallon and MPGe.

Taylor Marks

I don’t think there’s enough wiggle room to get below 3 seconds, which is the barrier for what Tesla deems “Ludicrous”. 3-4 seconds used to be called “Insane” by Tesla, and below 2 seconds is “Maximum Plaid”.

Going under 2 seconds will need autonomous mode since most drivers will probably not anymore be conscious…

0-100 km/h in 2s is 1.4G, untrained humans survive 17G for minutes before they loose consciousness

philip d

Don’t know how this is accurate but was looking up roller coasters I’ve been on and came across this on the Rockin’ Roller Coaster at Hollywood Studios Orlando: “0 to 60 is 3 seconds and you will experience 4.5 G forces, more than astronauts do on a space shuttle launch!” Other sources say the launch to 60 is in 2.8 seconds and between 4-5 Gs.

But all other information I can find about G forces and acceleration say that a 0-60 of 2 seconds will only produce 1.4 or so Gs like you are saying. Maybe there is a very brief 5 G load as weight shifts quickly from the horizontal force of this initial acceleration to vertical force from the first immediate loop right at the peak of this acceleration? So it’s maybe not the take off acceleration to 60 mph from the ride that produces the 4-5 Gs but rather the very brief transition from horizontal to vertical that causes this peak.

Here are the basic formulas for relating time, velocity, and acceleration:

Vfinal – Vinitial = a x t….or, solving for acceleration…..a = (Vf- Vi)/t

Vfinal = 60 mph
Vinitial = 0

1 g of acceleration = 32.2 feet/second/second

To correlate g’s with a final velocity in mph, you first have to convert mph to feet/second.

60 mph = 88 feet/second.

Accelerating from 0-60 in 3 seconds is an average acceleration of 88/3 = 29.3 ft/second/second. 1 g is 32.2 ft/second/second. So the Rockn’Roller Coaster is less than 1 g, at least for launch acceleration.

The g-forces the riders are subjected to when making turns, loops or diving through dips may be another story. That depends on velocity and turn-radius.

Pushmi-Pullyu

Right, the claim for 4-5 G’s on a roller coaster would not refer to the G’s experienced at launch, but rather later in the ride, when (for example) making a tight curve at the bottom of a drop.

If you are going to get technical, it is “lose,” not “loose”.
GrammarNazi
I guess that should be SpellingNazi, but you get my drift.

Bolt driver

A driver can handle 5 ish g’s prior to blacking out or having vision issues. I would guess there won’t be nearly enough traction to get close to that level of acceleration without special tires and a prepared surface.

Top-fuel dragsters do 0.5 seconds 0-100 km/h, at about 6g.

In other words, there is a *lot* of room for faster acceleration times in terms of driver resilience. The major challenge for a street-legal car is the tyres. (Unless you use add rocket boosters, like the New Roadster SpaceX option package 🙂 )

Rick Mann

So the difference between dual motor and performance appears to be how much juice they allow to go to motors and red brake calipers? The performance comes standard with same interior, same 18″ wheels/tires. Really wondering if a 1sec difference is now worth \$11,000 difference in price? Thoughts?

Pushmi-Pullyu

Diff’rent strokes for diff’rent folks. The only important question from Tesla’s viewpoint is how many buyers think it’s worth the \$11,000 upgrade, and whether that number is sufficient to justify putting the option(s) into production.

This is one of my favorite posts this year. I would love if you could dig deeper using the models.

I am on the fence with Dual Motor, not going to spring for the P even though I am dying for the white seats. So what I would love to see is a comparison for performance times between all the power trains (P, D, LR, SR).

My list would be:

0 – 30
0 – 60, Tesla’s claim and the model predictions
0 – 100
20 – 50 city passing
30 – 60 highway on ramp
60 – 80 highway passing
60 – 0 regen only unless you have a braking model
30 – 0 regen only unless you have a braking model

Or you if you share the model, I’ll go nuts myself, lol.

Thanks

Glad you liked it!

Actually, I have models set up for all the variation you listed, plus a hypothetical run for the currently-non-existent SR AWD version. The model only calcs acceleration, as of yet. We haven’t taken on regen braking performance other than calc’ing out energy recovery for long descents for a customized model we used when evaluating the Tesla semi’s range/b battery pack size and doing hypothetical runs from Fremont to the GF in Reno and back with empty and full loads.

I already have the 0-30, 0-60, and 0-100 times and qtr mile times. I’ll have to do a little tweaking to get the passing times you mentioned, but not a tough number to extract. Just adding a few calc cells to the table.

Check back tomorrow in the comments section. I’ll see if I can spring loose some time and re-run the calcs tonight and assemble the additional numbers.

Rick Mann

I’d love to see the numbers too. It’s so hard to spend the \$11k difference between Dual Motor and Performance when the only real standard difference is extra voltage being allowed to go to the same motor. It’s almost as if the Ludicrous mode is here, it’s just called Performance.

Pushmi-Pullyu

“Based on Electrek hacked number the battery is good for 500 hp so we have 5% margin. Leaving room for additional performance.”

Leaving at least a 5% margin to help avoid pack overheating and avoid overloading the fusible links or the power electronics, sounds like good engineering. In fact, I’ll bet the power electronics have more than a 5% margin in their power rating.

Bill Howland

I see nothing here regarding ESR of the battery system, nor minimum allowable input voltage to the inverter.

Nice analysis, but it seems to be missing the SR AWD option. What performance numbers do you think the SR AWD will have? Might it be close to the LR RWD numbers?

Ryan McCaffrey

George, out of curiosity where are you getting the idea that the P3D won’t have Ludicrous mode? Has this been confirmed somewhere?

Benjamin Orlowski

Math seems to work for Standard Range 3 AWD being the same 0 to 60 as the LR 3 RWD 5.1 ish but only having 2/3rds the battery. If you work back from 500hp to 2/3rds battery and 2 motors you have similar total output as Long Range RWD. If that assumption is true then the ludicrous P3D Theory works as well.