# Gearing and efficiency at RPM to/at 60 mph, the struggle is real



## dcb (Dec 5, 2009)

it depends how many hp you need at 60mph.

here are some swag graphs. you didn't say wheel diameter so you have to figure it out from there.

in this case on a motorcycle (prolly 12" radius wheel) the me1003 @72v can't even reach 60mph @5:1, but when geared for less wheel torque at 4.25:1 (300 wheel ft lbs)the dashed green line and the dashed purple line meet right at 60mph. 

if your trike has similiar cda as a motorcycle, you can expect similiar results. 2.5 is going to be way off, causing you to make a lot of motor torque(amps!) to try to maintain speed.


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## dcb (Dec 5, 2009)

also keep this graph in mind


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## mikesheiman (Jun 19, 2016)

In case it helps...

Wheel diameter is 30 inches (car tire) I believe, they are R15 tires.

CD is about 0.2...it's fully enclosed and teardrop shaped, but about as wide as a full sized car...think of it as a Prius, but lowered like a Vette, I'm guessing a frontal area of 25, may well be similar CDa to a motorcycle (lower CD, but higher frontal surface area).


I'm trying to make sense of the 72V 5:1 gearing graph...so the dotted purple line is required KWH to maintain speed and the dotted green line for the ME1003 is torque...or how should I read those two lines?


I suppose my real question is where should the green and purple lines meet at 60 mph with 15 inch wheels on a 1500 pound vehicle with a 0.2 CD?
If that (indeed?) represents where the least amps are needed to hold speed @ 72V.


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## dcb (Dec 5, 2009)

ok, so slightly taller wheels, you need a slightly higher ratio for comparison

15/12.63=1.188

4.25*1.188=5.0
so pretend the right graph is for a 5.0 ratio on the me1003 and the left is a 5.93 ratio.


with 300lb push (5:1 ratio on 15" radius tires), and lets say 2300lbs full of people and stuff you should be able to climb a 7.5 degree slope (i.e. 13% grade).

for the aero stuff I just use an online calculator. But since you are rolling you can do coastdown tests or other measurements to get a better picture of hp required at speed. EDIT: AND ALSO TO TEST IF YOUR AERO MODS ACTUALLY DO ANYTHING!!! look up A-B-A testing.

http://www.wallaceracing.com/Calculate HP For Speed.php


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## Duncan (Dec 8, 2008)

Hi Mike
How did you get a CD of 0.2?

That is incredibly good!

How did you test it?


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## mikesheiman (Jun 19, 2016)

The main differences that allow the CD are
*) Tapered rear end
*) Continuous sloped hood and roof with no bumper/"brick" in front or back
*) Perfectly smooth bottom end
*) Tightly space wheel wells and no third wheel well in back


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## mikesheiman (Jun 19, 2016)




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## Duncan (Dec 8, 2008)

Mike
Your taper is far far too abrupt to get the sort of CD you are talking about

The air will not follow that type of curve

I predict a CD of just above 0.3 or worse

Do you have any test results??


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## dcb (Dec 5, 2009)

yah, sorry to say but people really underestimate how hard aero is. But 2.0 is like ev1 level coefficient of drag, and they had huge teams and lots of money and time (and equipment and tools and experience). You really can't just throw a number out there on a new design without actual testing. Especially when you are putting such a small motor in there with so little room for error on the power requirements.


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## mikesheiman (Jun 19, 2016)

Wait, are you saying the taper can actually hurts the car that much?
Consider there are *hatchbacks with drag coefficients of around 0.3, provided they have a/the continuous hood to windshield to roof to rear line (egg shaped) my design also has.*

Because an *EV1 doesn't taper inward at all*, how is it anything else than just a big block (air pressure vacuum) in the lower half back of the car where the lights and bumper are. Ditto with the Model S. Not to mention there's no flat front bumper area in the trike like in normal cars, just a smooth curve all the way to the floor.

As for why the 0.19 EV1 would only be slightly better than my design especially despite the low sloping rear end possible from being a 2 seater? 
The EV1has bumpers (dead zones), a trunk, a discontinuous/turbulent line between the hood and windshield and again from the roof to the rear window, full sized mirrors (mine are 1/4 sized streamlined mini superbike mirrors), and a windshield. *All the above designed, I presume, to make the EV1 look and function (hood style and also trunk/spacewise) more like a normal car as a prerequisite to aerodynamics.* Granted it's amazing they got the CD so low despite all those stylistic self-limitations to make it "normal".

* Is there a reason tapering (e.g. too sharply) would actually make a/the vacuum much worse/more-turbulent than no effort to taper at all or that they would cancel out all of the above advantages or that the above advantages would be null and void?

*If that's true, I may need to duct air from other parts of the car to the/that dead/vacuum zone in the rear somehow (From the bottom? From the removable sunroof? Maybe even some from the top of the side area?). If that yields great advantages, thanks for the awesome tip and I'll get right to fixing that.

I do know this design has seen my puny *ME1003 motor propel this 1500 pound trike to 75 mph on flat road with no tailwind* *or other aerodynamic cheating*. If that's not due to better-than-average aerodynamics, I really wonder how that could happen.


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## mikesheiman (Jun 19, 2016)

Oops..duplicate post.


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## dcb (Dec 5, 2009)

mikesheiman said:


> I do know this design has seen my puny *ME1003 motor propel this 1500 pound trike to 75 mph on flat road with no tailwind* *or other aerodynamic cheating*. If that's not due to better-than-average aerodynamics, I really wonder how that could happen.


what rpm are you doing at 75mph? 20 drive, 36 driven, 15" wheels? 1500?

how many motor volts and amps were there?

what is the efficiency at that operating point?

what is the resulting output power?

fudging around with the aero calc, what CDA do you wind up with for that power at 75 mph?

how did you determine the frontal area?


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## dcb (Dec 5, 2009)

fyi, my swag, assuming 1500 rpm, 500 amp capable controller, 72 volt pack, is ~15hp.

fudging with the hp vs speed calc:
i threw some numbers in, feel free to tweak, as long as CD * A is the same you should be close to 15 hp:

Coefficient of Drag	.35
Frontal Area of Car	15 Sq/Ft
Weight of Car	1500 Lbs
Velocity of Car	75 MPH

and it came back with 15 hp required.

anyway, assuming CD*A is in the ballpark, you can figure out the hp needed for 60mph as top speed with the same calculator, in the upper right graph the dotted purple line would move up 3.3kw or so

basically what you have done with 20:36x15 is taken that dashed green line and stretched it horizontally so far to the right that it intercepted 75mph while still climbing to 11kw-ish, and you left a whole lot of area under the curve (power) out of the equation. you stalled out at 11kw without ever seeing anything like 25kw. 5:1 is going to feel like night and day probably.


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## mikesheiman (Jun 19, 2016)

> what rpm are you doing at 75mph? 20 drive, 36 driven, 15" wheels? 1500?


Think it was 1400, but somewhere very close to there.



> how many motor volts and amps were there?
> what is the efficiency at that operating point?
> what is the resulting output power?


72 volt system, possibly with voltage sag as they're lead acids, unsure about amp usage and the rest.
Turns out my charger fried some of my old 12v gauges (original 72v-12v converter had too large a margin of error for volt reduction and apparently over-volted them while charging) so I have to get new ones before I can capture those amp at speed ratings. Will forward them soon as I get them.



> how did you determine the frontal area?


 *I'm airing on the side of caution with 25, it may well be a bit lower. * It's virtually the same width (74 inches), height (49 inches), and hood/windshield angle *as a C7 Corvette*, which supposedly *has a 21 square foot frontal area*. 

Whether everything turns out to be good or not (my goal was a CD of 0.20 or under, actually started the project somewhat using the EV1 as a hint it's possible without an extreme custom tapered shape like the Edison2's), *either way I'm really curious how to improve any taper/vacuum issues for the future and still really curious if/how having a taper vs. no taper can actually hurt aerodynamics.

* Also, thanks for all your hard work checking all this through.*

I also asked about the rear shape on ECOMODDER's aerodynamics forum for grins.
*


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## mikesheiman (Jun 19, 2016)

Also, using 
http://www.tritrack.net/horsePower.html

Plugging in 1500 pounds, 1 passenger of 150 pounds (me), 0.2 CD, and a* 25 square foot frontal* area I get *19.5 horsepower* needed to maintain speed.

Plugging in 1500 pounds, 1 passenger of 150 pounds (me), *0.3 CD (Duncan estimate)*, and a* 25 square foot frontal* area I get *26.5 horsepower* needed to maintain speed at 75. Huge difference.


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## mikesheiman (Jun 19, 2016)

> you stalled out at 11kw without ever seeing anything like 25kw. 5:1 is going to feel like night and day probably.


Ha, admittedly I'm quite confused...so you're saying 5:1 isn't going to require more amps even at that speed (hitting about 15HP or 11kw usage to cruise at 75 mph), but will give significant increase in available power/torque even approaching such a high speed?


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## dcb (Dec 5, 2009)

I added some notes fyi, I think you stalled out at about 11kw at 75mph, and never came close 25kw.

I inferred it from the motor graphs at 1500rpm fyi and swaged 15hpish.

if you move the dotted purple line up 3.3kw you will have to back of from 5:1 a little to hit 60mph, not a lot. 2.5:1 IS still a bad choice for 60mph top speed, 4.5 would be the lowest probably.

what make/model/year is the rear sprocket off of? you can cross reference via jtsprocket catalog and probably find a bigger one on ebay for cheap.


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## dcb (Dec 5, 2009)

mikesheiman said:


> Ha, admittedly I'm quite confused...so you're saying 5:1 isn't going to require more amps even at that speed (hitting about 15HP or 11kw usage to cruise at 75 mph), but will give significant increase in available power/torque even approaching such a high speed?



climb up the dotted green line in the upper right graph. stop when you get to 11kw, that is about where you stopped accelerating to 75mph (your goofy ratio is 75mph when the graph says 21mph). look at all that area under the dashed green curve that you never touched.

5:1 (slightly less for 60mph top speed) is going to use the same current and give you 4x the acceleration with a 60mph top speed. or get you there in the same time with 4x less current.


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## mikesheiman (Jun 19, 2016)

> 5:1 (slightly less for 60mph top speed) is going to use the same current and give you 4x the acceleration with a 60mph top speed. or get you there in the same time with 4x less current.


So there's no efficiency benefit, even for cruising, gained by higher gearing (lower reduction ratio) beyond what's needed to reach the cruising speed?

In other words, high RPM is always better (for both acceleration and cruising efficiency), so long as the vehicle reaches the desired top speed with the gearing?


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## dcb (Dec 5, 2009)

mikesheiman said:


> So there's no efficiency benefit, even for cruising, gained by higher gearing (lower reduction ratio) beyond what's needed to reach the cruising speed?


Not really no, doesn't seem to be. motors are pretty bad at efficiency at both low rpm and low load, and you trade rpm for load with gearing. 

whereas allowing the motor to rev higher makes more power and wheel torque. Allowing it to spin up it will create back EMF (voltage) and reduce the current, that is why the torque drops off on those graphs, it can no longer deliver 500 amps or so from the pack voltage. (note that permanent magnet and shunt motors drop off faster).

edit: plus letting it spin up means the internal fan is moving more air and keeping it cooler.


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## Duncan (Dec 8, 2008)

Hi Mike
If you look on the Ecomodder site you can see the type of angles that are required to prevent airflow separation in order to achieve the sort of drag numbers you are looking for

http://ecomodder.com/forum/tool-aero-template.php


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## mikesheiman (Jun 19, 2016)

> The type of angles that are required to prevent airflow separation


* Yeah, funny, it's virtually an exact match to their template if the car is flipped the opposite direction and the (sideways) taper ignored e.g. "reverse teardrop"!
*
Thing is, realistically, *a car matching that teardrop shape (0.15CD with wheels) *would have to be extremely long to keep the roof over the rear passenger occupants' heads and looks absolutely nothing like the EV1s or Prius's (far as rear end length) nor does the template show the (harmful?) effects of short length tapering like my car's vs. no tapering at all. 

So far this is what I have learned:
*) Same as suspected, the taper is longer than ideal (taper as an attempt to allow air from the sides to somewhat rejoin in the center instead of leaving a vacuum in the rear area). *No one on either site seems to have a decent answer why this is such an issue when cars like the EV1 have no attempt at a rear taper at all!
**) The only other turbulence zone noted is behind the front wheels, apparently it should not curve downward at all as it *creates an, if small vacuum a couple of inches tall behind the front wheel. 

Should I 
*A) *Simply eliminate the taper completely*, *leaving a Prius-shaped blocky full width very rear end* 
B) Start it inwards at an earlier point (the frame would let me make the taper about twice as long)
C) Smoothen the area from the front to the back on the sides into a straight line with no dip behind the front wheel(s)?

I'm looking for things *I can actually do to improve this shape, *since no standard length 4 door car on the road even vaguely matches the ideal fishtail shape, including the EV1 or Prius.

*I am planning to TUFT/streamer test the shape for turbulence zones.


*


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## Duncan (Dec 8, 2008)

Hi Mike

What you need to look at

Your front wheel arches go down and then back up - Don't go down - the slope is too steep you will get separation
your point (c)

Where you curl the back in from the side and downwards is far far too steep - move in much more gently
Then when you get as far back as you want length wise - cut it off 
It's called a Kamm-tail or Kammback
After Wunibald Kamm
https://en.wikipedia.org/wiki/Wunibald_Kamm

This is the basis for most fairly low drag cars - if you look at a Prius you will see that it slopes downwards and the sides taper inwards - until it truncates
- I think you need rounded edges on the truncation

Fairing in the wheel wells would make a lot of difference as well - and you should look at the wheel openings underneath the car - make them as small and close to the wheel as you dare


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## mikesheiman (Jun 19, 2016)

> Your front wheel arches go down and then back up - Don't go down - the slope is too steep you will get separation
> your point (c)


Indeed. Wondering how to accomplish that most easily...layer over with something or completely redo that fiberglass?





> Then when you get as far back as you want length wise - cut it off
> It's called a Kamm-tail or Kammback


Yes, I've heard of Kammbacks.
In other words, I'd be better off simply following the beginning of a teardrop rear shape 
and cutting off than making a/the sudden curve downward after the end of the teardrop shape?

Can I mimick this with a *rear spoiler shaped like the beginning of a rear teardrop (ALA the Ford Focus hatchback* like on 








...or do I actually have to put a flat edge back there and redo the back end center fiberglass?



Far as the taper...are you implying I should taper less at a much smoother transition and cut off in the rear area in a very similar fashion, but sideways?

Also again, I ask, it the taper I have now worse aerodynamically than, say, simply making a block/wall-shaped area where the back of the rear seat is and having the rear wheel stick out by itself?

* The general impression I'm getting is a Kammback-ended teardrop rear slope beats a teardrop followed by a steep drop downward or inward, correct?*


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## dcb (Dec 5, 2009)

is the gearing making any more sense? I would like to bow out of the discussion at this point as there isn't any explanation of how you are going to baseline your existing cd and A and RR and validate your changes and your testing procedures.


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## mikesheiman (Jun 19, 2016)

> is the gearing making any more sense? I would like to bow out of the discussion at this point as there isn't any explanation of how you are going to baseline your existing cd and A and RR and validate your changes and your testing procedures.


Yes, the gearing is making sense now.

Oddly enough, it's contrary to what the engineer I'm working with appears to have suggested, perhaps he's mistakenly thinking of how ICE engines handle excessive RPMs and/or load vs. electric motors.

*Far as drag,* I'm going to test how much *power (on my ammeter) the car takes to hold at higher speeds* and see what CD/frontal area value multiplied combination gives the same figure I did via the Tritrack calculator on http://www.tritrack.net/horsePower.html for a 1500 pound vehicle. I'm assuming a *0.012 rolling resistance as rated for the Goodyear Eagle tires I'm using.*

Once I have that I'm going to throw on some cheap temporary aero-mods, like a wood-glue coated cut corrugated cardboard curved box over the rear tire to form a kammback *and compare the HP needed for speed before and after the mods. *

If the corrugated cardboard plastic works, I will redo the actual body to fit the best tested mold.


The aerodynamics issue is really getting on my nerves, especially since I worked with an engineer who assured me the car shape was teardrop-based and should easily get a CD under 0.25. The oversight of the front wheel turbulence issue especially makes me wonder what he was thinking (that it just "looks cooler"?!). I'm not just going to leave this one hanging...if I have to chop off the entire sides of the car and redo everything but the front fiberglass panel to make it work well, so be it.

I'm also thinking of making/gluing-in? some sort of insulation fiberglass mesh around the wheel well area simply to keep air out of those around wheel pocket areas (right now they're as close as I can get them without scraping the tire on turns, but I wonder if I can have them slightly scrape fiberglass insulation without knocking it out).


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## samwichse (Jan 28, 2012)

mikesheiman said:


> *a car matching that teardrop shape (0.15CD with wheels) *would have to be extremely long to keep the roof over the rear passenger occupants' heads and looks absolutely nothing like the EV1s or Prius's (far as rear end length) nor does the template show the (harmful?) effects of short length tapering like my car's vs. no tapering at all.
> 
> *No one on either site seems to have a decent answer why this is such an issue when cars like the EV1 have no attempt at a rear taper at all!
> *


*

I don't know what you're talking about but the EV1 tapers along its entire length after the side view mirrors.










The rear wheels have a narrower track than the fronts.

The first gen insight also tapers from this same point. The taper is not as extreme as the ev1, but the rear wheel track is also narrower than the front...

















In both cases terminating in a clean kammback
https://en.m.wikipedia.org/wiki/Kammback*


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## dain254 (Oct 8, 2015)

Instead of an ammeter, I use a thing called a "cycle analyst". they are $130 and ship from Canada in about a day, tells you MPH, miles, battery cycles, battery SOC, instantaneous power draw, watts/mile... all kinds of stuff! Here is a link

http://www.ebikes.ca/product-info/cycle-analyst.html

You would want one with a remote shunt, I'm not sure what everyone else on the forum uses, but these have worked great for my projects!

From your extremely high gear ratio you are likely pulling the peak that the motor will allow basically the entire time you are on the throttle!


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## mikesheiman (Jun 19, 2016)

I stand corrected, at least technically, if not also to a significant functional degree. Looking at the top of the EV1 (before I'd seen only the front/sides and it looked cosmetic at best), I indeed notice a taper and significant front/rear wheel track difference, if not significant enough to be obvious at a glance.

My vehicle has the challenge of going from some 71 inches width for the rear seats to trying to, without air stream discontinuity, approach the width of the tire itself.

* So starting at 71 inches at back of the rear seat area with a flat side, about how many inches wide would you estimate I can/should be along a/the curve at the back of the rear wheel (about 3 feet behind) without it being so sharp an angle it causes air-stream separation/discontinuity?*


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## dain254 (Oct 8, 2015)

My rear tire is 26" OD so I was definitely running out of RPM w a 5:1 ratio, At top speed I would never pull more than 12-13kw up hill and about 9-10 on the flat due to the motor being topped out (~50mph). I would only see the 20-21kw peak in the 10-30mph range accelerating.

Aero is definitely the cause of my top speed issues, my vehicle is basically a wedge shape - I designed it for open top style! I'll push through my speed barrier with a hefty dose of horsepower via a big brushless motor and lithium batteries to feed it!


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## dcb (Dec 5, 2009)

oh, how are you (Mike) measuring mph?


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## mikesheiman (Jun 19, 2016)

Measure MPH via GPS for now on my smartphone.


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## akseminole (Jan 5, 2014)

Since you are on the quest for better aerodynamics and are into experimenting to get there.
You could try plasma actuators.
http://www.diyelectriccar.com/forums/showthread.php/plasma-actuators-better-aerodynamics-167498.html


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## dcb (Dec 5, 2009)

Lol .


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## sunworksco (Sep 8, 2008)

I'm planning to use 26" diameter wheels, with an 8-1 gear ration.
My car will only weigh around 450Lbs. It shouldn't be to slow, off the mark.
This is with a 15Kw motor and a 100volt battery pack.
Does this seem realistic?


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## dcb (Dec 5, 2009)

8:1 is kind of huge, what motor is it? got any torque graphs for it?


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## sunworksco (Sep 8, 2008)

Astrolight 15Kw


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## sunworksco (Sep 8, 2008)

120volt battery pack.
Hopefully the large cell graphene battery packs will be out there, when I'm ready to install....


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## dcb (Dec 5, 2009)

I'm just gonna pretend you have 12" radius wheels cuz I'm lazy 

but using 4t (100V & 160A) and 8:1


that 17 in/oz per amp @160 amps translates to 116 pounds of thrust (after 8:1), which isn't bad for a 400 lb vehicle (including driver?) lets say 500 w/driver, so 
arcsine(116/500)=13.5 degree max slope you can climb.

and if it is aerodynamic enough, you will top out at ~71mph. (100v * 80rpm/v = 8000 rpm)

note: 100v might be rms, in which case you need a 140v pack.


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## sunworksco (Sep 8, 2008)

Thanks!
My wheels will be 26" Ducati, with Michelin touring tires.
The body will be reverse of the image in the attached drawing. Round end reversed to front.
It will be 12ft. overall length X 27" width X 26" heigth


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## dcb (Dec 5, 2009)

Hopefully Mike doesn't mind us discussing this here, but I'm curious what your design goals are? (and also your motor selection process)

max top speed? (slow off line)
figure cda and rr, and set gearing so peak power crosses power required.


max acceleration off the line with a slower climb (i.e. like shifting)?
don't use permanent magnet motor, or else you have to use stator current for field weakening.

with that level of streamlining you won't need a lot of power to go fairly fast, so a different kind of motor (series or ac) will give you even better acceleration off the line and/or more top speed (note the solid purple and red lines in the graphs in post #2 for the DD es15 and the ac20), the permanent magnet motors kind of hit a wall by comparison.

i.e. looking at the 300ft lb graph in the upper right, the single agni, even though it makes a bit more peak power than the DD, it crosses the power required line at about 55mph, where the series wound DD crosses it at 75mph. and the ac-20 (induction) is only a little higher peak power than the agni, but it crosses the power required graph at over 100mph. and they all have the same acceleration (300 ft lbs) up to about 42 mph.

just thinking out loud.

Note: the dashed purple line is different for every vehicle (kw required), it is a function of rolling resistance, frontal area, and coefficient of drag, which you can get a good approximation of with coastdown tests and a long zoom picture if you want to eliminate some guesses and trial and error.


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## Duncan (Dec 8, 2008)

Hi Sunworks

Your open wheels will contribute a huge amount of drag - the problem is the top of the tire is going at twice vehicle speed and drag goes up with the square of speed

As drawn your car will have a poor drag coefficient even without the wheels as the all important rear taper is too sharp - the air will separate and the tail will do nothing


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## dcb (Dec 5, 2009)

it is pretty low frontal area though, even the tires, though they could be better.

2d analysis isn't great by a long shot, and my squinting at the fuselage probably doesn't help with low res outline, but here is what the online flowillustrator did with the attached (video id 8631cd3a): http://video.flowillustrator.com/14675071548631cd3a.avi

but if you guys really want to play aerodynamicists (as opposed to fortune teller), you really should learn openfoam or some 3d flow modelling, or get a windtunnel at least and test some clay shapes.


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## electro wrks (Mar 5, 2012)

Is this what your looking for in aero body shape? : https://shiftev.com/index.php/shop/small-vehicle-sytems/cyclone-body-fiberglass-black-detail.html


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## sunworksco (Sep 8, 2008)

I will change the rear taper to a small Kamback.
Just wide enough to get some good motorcycle design lighting.
And the top rear body section will have a tapering headrest, tapering down to the end. It will slightly resemble a 1940's Indy 500 race car.
Here is the McClaren Rocket car.
I want to keep the flat slab sides of the original design, ala Morgan reverse-trike.
Makes fabrication much easier, too.
I'm planning to place the batteries under the subfloor, for lower CG.
I'm going with inboard coil-over shocks, from wrecked Ducati motorcycles.
That opens up the airflow and keeps the shocks clean.
It will have a full smooth belly pan.


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## Duncan (Dec 8, 2008)

That would work

But you will need to cover those wheels! - a close fitting whole wheel spat that is attached to the suspension and moves with the wheel would be best


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## sunworksco (Sep 8, 2008)

Hopefully, by the time I'm ready to roll, the graphene fiber cloth will be available for the wheel covers. I'm planning to use DP suspension and he can build the uprights with the wheel cover bracket hardware.
Here is the E-Wolf E-1


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## sunworksco (Sep 8, 2008)

From the rear....


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