Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-14 Thread Peri Hartman via EV

That's pretty impressive ! I want a new chess set :)

<< Want to know about the effects of leaf blowers ? 
https://quietcleanseattle.org/ >>


-- Original Message --
From: "Peter VanDerWal via EV" 
To: "Electric Vehicle Discussion List" 
Cc: e...@vanderwal.us
Sent: 13-Jul-20 8:34:47 PM
Subject: Re: [EVDL] Solar powered vehicle panel requirements.


Oops, forgot to post a link to the photo

https://sourcegraphics.com/files/2914/8780/2404/grey_rook.jpg


 Here is a hires picture of a rook printed with an MSLA printer, realise that the 
actual piece is 2"
 tall.

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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-13 Thread Peter VanDerWal via EV
Oops, forgot to post a link to the photo

https://sourcegraphics.com/files/2914/8780/2404/grey_rook.jpg

> Here is a hires picture of a rook printed with an MSLA printer, realise that 
> the actual piece is 2"
> tall.
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-13 Thread Peter VanDerWal via EV
July 12, 2020 4:11 PM, "Peri Hartman via EV" 
 
> Using a small scale wind tunnel just triggered an idea. How hard would
> it be to make a 3D printed model of your car ? (Pretty hard when you
> have to consider that it's every tiny bump that makes a difference in
> wind, but doable.)


Some of the new MSLA printers can do very tiny voxels.  I recently purchased an 
Elegoo Mars and it's minimum voxel size is 47x47x20 microns, which is too small 
for these old eyes to make out layer lines even with glasses on. 
Parts come out of it and look like they came from a high quality mold (i.e. no 
mold lines), with intricate details.
I was fairly impressed with what I was getting from FDM printers, but this 
thing is amazing.

Here is a hires picture of a rook printed with an MSLA printer, realise that 
the actual piece is 2" tall.
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-13 Thread Peter VanDerWal via EV
As I recall for research I did 20 years ago, as you scale down the model you 
have to increase the wind speed to get the same drag effects.  Using a model 
that is smaller than 1/4 scale results in wind speeds that are impractical.
I don't remember the exact details but it has something to do with the 
"Reynolds number"

As I recall you can partially offset this effect by using a more viscous fluid, 
so for really small models you might be able to use a 'water tunnel' instead.

Anyway, around that time (20 years ago) it became practical to do the 
aerodynamic modeling using a computer and get very accurate results, so I lost 
interest in using wind tunnels.

July 12, 2020 4:11 PM, "Lee Hart via EV"  wrote:

> From: Peri Hartman via EV 
> 
>> Using a small scale wind tunnel just triggered an idea. How hard would
>> it be to make a 3D printed model of your car ? (Pretty hard when you
>> have to consider that it's every tiny bump that makes a difference in
>> wind, but doable.)
> 
> How about if he finds a plastic model of his car? They should be pretty 
> darned close to the real
> thing. Put that in a wind tunnel.
> 
> Then as you say, you could experiment with various aero mods and trailers.
> 
> Lee Hart
> 
> --
> Excellence does not require perfection. -- Henry James
> --
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-12 Thread Lee Hart via EV
From: Peri Hartman via EV 
>Using a small scale wind tunnel just triggered an idea. How hard would 
>it be to make a 3D printed model of your car ? (Pretty hard when you 
>have to consider that it's every tiny bump that makes a difference in 
>wind, but doable.)

How about if he finds a plastic model of his car? They should be pretty darned 
close to the real thing. Put that in a wind tunnel.

Then as you say, you could experiment with various aero mods and trailers.

Lee Hart

--
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--
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-12 Thread Peri Hartman via EV
Using a small scale wind tunnel just triggered an idea. How hard would 
it be to make a 3D printed model of your car ? (Pretty hard when you 
have to consider that it's every tiny bump that makes a difference in 
wind, but doable.)


Anyway, having a scale model would allow inexpensive wind tunnel 
testing. You could test, for example, the effect of a trailer. Or 
raising the suspension of your vehicle a bit. Or adding an air dam in 
the front. Or adding roof racks.


Peri

<< Want to know about the effects of leaf blowers ? 
https://quietcleanseattle.org/ >>


-- Original Message --
From: "Lee Hart via EV" 
To: "Electric Vehicle Discussion List" 
Cc: "Lee Hart" 
Sent: 12-Jul-20 2:26:39 PM
Subject: Re: [EVDL] Solar powered vehicle panel requirements.


When I put a small flat 4'x6' utility trailer on my Prius, the
mileage went from 55 down to 40!  And that was with no load or added
wind drag other than the trailer. So it is quite silly to think one
can add a trailer to get SOlar without losing more in the trade!


Aerodynamics is funny stuff. It's not at all intuitive, unless you've studied 
aeronautical engineering.

A flat trailer might seem like it would have low wind resistance; but a square 
front edge and rough surface can create a considerable amount of drag. Open 
tires without fenders or wheel wells also have a lot of wind resistance; 
especially at the top of the tire, which is moving forward at *double* the 
speed of the vehicle. The bottom of a trailer is also rarely flat or smooth; it 
will have lots of projections.

Some museums have little wind tunnel setups, where you can insert verious 
shapes, and read the drag and lift on meters. Some include little smoke 
generators, so you can see where laminar flow breaks into turbulence, and the 
big increase in drag it causes.

Lee Hart

-- If happiness is on your mind, here's a daily list to find:
 - something to do
 - something to look forward to
 - someone to love
 - someone to take good care of
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Lee Hart, 814 8th Ave N, Sartell MN 56377, www.sunrise-ev.com
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-12 Thread Lee Hart via EV

When I put a small flat 4'x6' utility trailer on my Prius, the
mileage went from 55 down to 40!  And that was with no load or added
wind drag other than the trailer. So it is quite silly to think one
can add a trailer to get SOlar without losing more in the trade!


Aerodynamics is funny stuff. It's not at all intuitive, unless you've 
studied aeronautical engineering.


A flat trailer might seem like it would have low wind resistance; but a 
square front edge and rough surface can create a considerable amount of 
drag. Open tires without fenders or wheel wells also have a lot of wind 
resistance; especially at the top of the tire, which is moving forward 
at *double* the speed of the vehicle. The bottom of a trailer is also 
rarely flat or smooth; it will have lots of projections.


Some museums have little wind tunnel setups, where you can insert 
verious shapes, and read the drag and lift on meters. Some include 
little smoke generators, so you can see where laminar flow breaks into 
turbulence, and the big increase in drag it causes.


Lee Hart

--
If happiness is on your mind, here's a daily list to find:
 - something to do
 - something to look forward to
 - someone to love
 - someone to take good care of
 - and misbehave, just a little
 --
Lee Hart, 814 8th Ave N, Sartell MN 56377, www.sunrise-ev.com
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-12 Thread Willie via EV




On 7/11/20 9:17 PM, Robert Bruninga via EV wrote:

When I put a small flat 4'x6' utility trailer on my Prius, the mileage went
from 55 down to 40!  And that was with no load or added wind drag other
than the trailer.


There is a LOT of variance in trailers.  I have two small flat trailers 
with the utility type tires/wheels (12", I think) rather than larger 
(13"+) car style wheels.  Pulling empty with either an imiev or a Tesla, 
you hardly notice an impact on range, under 5%.  Loaded with ~1000 
pounds that sticks up ~2', the impact may be close to 10%.


Still, that ~5% may well be enough to wipe out any benefit from having 
PV panels.


I also have a "small" teardrop camping trailer that costs 25-30% when 
pulled by a Tesla.


https://wmckemie.blogspot.com/2020/06/pulling-unlicensed-unlighted-trailer-at.html

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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-12 Thread Lawrence Rhodes via EV
 It has to be big enough and light enough and aerodynamically sound. The 
formula is 850 pounds and 1.5kw battery and a 1.5kw solar panel. CD of .16.  
Lawrence Rhodes

On Saturday, July 11, 2020, 7:18:26 PM PDT, Robert Bruninga 
 wrote:  
 
 When I put a small flat 4'x6' utility trailer on my Prius, the mileage went 
from 55 down to 40!  And that was with no load or added wind drag other than 
the trailer.
So it is quite silly to think one can add a trailer to get SOlar without losing 
more in the trade!
Bob
On Fri, Jul 10, 2020 at 12:17 PM paul dove via EV  wrote:

 That math seems wrong to me. 3200 Wh at 25Wh/m = 12.8 miles not 1 mile.

    On Friday, July 10, 2020, 8:22:02 AM CDT, Tom Mandera via EV 
 wrote:  

 There are 400w panels out that are roughly 7'x3.5'  So a rather 
reasonable 7'x7' trailer could produce 800w, which is a good amount of 
power - but not nearly enough.

Assuming they're mounted flat, that's 800w at high noon, and less at 
every other part of the day.  We could expect something like 3.2kwh / 
day of production, or roughly a 1 mile extension in range.

To get the 12kw needed, we need at least 15 times that, or 105' long 
trailer, 7' wide.  Then we could drive continuously at around the noon 
hour for around an hour, on a good sunny day.


Sadly, as you said, it's a math problem..

On 7/10/20 12:21 AM, Lawrence Rhodes via EV wrote:
> The math problem here is consumption over time. A solar racer with a 5 
> passenger capacity 850 pound weight with a coefficient of drag of .16  
> rolling on moped wheels with a 1.5kw panel and 15kw battery can attain 45mph 
> continuously without using battery power. A Nissan Leaf going 55mph achieving 
> 5 miles per kwh would(if I got my math right) need 12kw continuously to keep 
> that speed in full sunlight.  Of course the battery is a buffer that will 
> allow you to do faster speeds and climb hills. I suspect some sort of Pop 
> tent trailer might be a good combination for the Cyber Truck. 450.5 sq. ft. 
> is the maximum size of a trailer. A pop tent that size would be quite a 
> mansion. However that might only produce 5 to 6kw. Enough to charge and 
> extend but not to run continuously.  Weight must be reduced and coefficient 
> of drag lowered. It's a math problem.  Lawrence Rhodes
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-11 Thread Robert Bruninga via EV
When I put a small flat 4'x6' utility trailer on my Prius, the mileage went
from 55 down to 40!  And that was with no load or added wind drag other
than the trailer.

So it is quite silly to think one can add a trailer to get SOlar without
losing more in the trade!

Bob

On Fri, Jul 10, 2020 at 12:17 PM paul dove via EV  wrote:

>  That math seems wrong to me. 3200 Wh at 25Wh/m = 12.8 miles not 1 mile.
>
> On Friday, July 10, 2020, 8:22:02 AM CDT, Tom Mandera via EV <
> ev@lists.evdl.org> wrote:
>
>  There are 400w panels out that are roughly 7'x3.5'  So a rather
> reasonable 7'x7' trailer could produce 800w, which is a good amount of
> power - but not nearly enough.
>
> Assuming they're mounted flat, that's 800w at high noon, and less at
> every other part of the day.  We could expect something like 3.2kwh /
> day of production, or roughly a 1 mile extension in range.
>
> To get the 12kw needed, we need at least 15 times that, or 105' long
> trailer, 7' wide.  Then we could drive continuously at around the noon
> hour for around an hour, on a good sunny day.
>
>
> Sadly, as you said, it's a math problem..
>
> On 7/10/20 12:21 AM, Lawrence Rhodes via EV wrote:
> > The math problem here is consumption over time. A solar racer with a 5
> passenger capacity 850 pound weight with a coefficient of drag of .16
> rolling on moped wheels with a 1.5kw panel and 15kw battery can attain
> 45mph continuously without using battery power. A Nissan Leaf going 55mph
> achieving 5 miles per kwh would(if I got my math right) need 12kw
> continuously to keep that speed in full sunlight.  Of course the battery is
> a buffer that will allow you to do faster speeds and climb hills. I suspect
> some sort of Pop tent trailer might be a good combination for the Cyber
> Truck. 450.5 sq. ft. is the maximum size of a trailer. A pop tent that size
> would be quite a mansion. However that might only produce 5 to 6kw. Enough
> to charge and extend but not to run continuously.  Weight must be reduced
> and coefficient of drag lowered. It's a math problem.  Lawrence Rhodes
> > -- next part --
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-11 Thread Lawrence Rhodes via EV
From: paul dove 

Cute! The problem is to design one that meats current crash safety requirements 
and still be light and efficient.

The Stella racers are built like Formula 1 and use 5 point belts. Certainly 
legal in Holland and probably here. They would fall under at least special 
construction.  I could be wrong but if a car has 5 point racing belts air bags 
are not required. Lawrence Rhodes



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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-11 Thread paul dove via EV
Cute! The problem is to design one that meats current crash safety requirements 
and still be light and efficient.

Sent from my iPhone

> On Jul 11, 2020, at 10:58 AM, Lee Hart via EV  wrote:
> 
> Lawrence Rhodes via EV wrote:
>> It's a math problem that can't be solved. At least not with today's
>> technology. I think it is a weight problem that can be solved with today's
>> technology...at least by students in Holland. Of course you can't do it with 
>> the piggy Tesla's and Bolts. Something much lighter. Lawrence Rhodes 
>> https://solarteameindhoven.nl/
> 
> I'd characterize it as a problem that can't be solved with traditional old 
> solutions (heavy steel cars, etc.) But it can be solved with new technology, 
> as has been demonstrated many times by solar cars. It just requires people to 
> think outside the box.
> 
> Heck, batteries are good enough that you could even do it without the solar 
> panels. Or even less...
> 
> "I've invented an amazing machine that can transport people over a hundred 
> miles a day. It's clean, quiet, non-polluting, inexpensive, and uses no 
> fossil fuels, motors, or batteries. I call it a 'bicycle'".
> 
> Lee Hart
> 
> -- 
> If happiness is on your mind, here's a daily list to find:
> - something to do
> - something to look forward to
> - someone to love
> - someone to take good care of
> - and misbehave, just a little
> --
> Lee Hart, 814 8th Ave N, Sartell MN 56377, www.sunrise-ev.com
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-11 Thread Robert Bruninga via EV
My 3 solar panels (240W) on my Franken-Volt add about 30 miles a week.
See http://aprs.org/my-EVs.html
Bob

On Sat, Jul 11, 2020 at 4:11 AM Lawrence Rhodes via EV 
wrote:

> To: ev@lists.evdl.org
> Subject: Re: [EVDL] Solar powered vehicle panel requirements.
> Message-ID: 
> Content-Type: text/plain; charset=utf-8; format=flowed
>
> It's a math problem that can't be solved. At least not with today's
> technology.
> I think it is a weight problem that can be solved with today's
> technology...at least by students in Holland. Of course you can't do it
> with the piggy Tesla's and Bolts. Something much lighter. Lawrence Rhodes
> https://solarteameindhoven.nl/
>
>
>
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-11 Thread Lee Hart via EV

Lawrence Rhodes via EV wrote:
  I commonly get much better range. My indicator of accumulated data says 4.9 miles per kwh. Your mileage may vary. Lawrence Rhodes-- 


That's exactly the same as our 2013, Lawrence. We must be doing 
something right.


Lee Hart
--
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 - something to do
 - something to look forward to
 - someone to love
 - someone to take good care of
 - and misbehave, just a little
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-11 Thread Lee Hart via EV

Lawrence Rhodes via EV wrote:

It's a math problem that can't be solved. At least not with today's
technology. I think it is a weight problem that can be solved with today's
technology...at least by students in Holland. Of course you can't do it with 
the piggy Tesla's and Bolts. Something much lighter. Lawrence Rhodes 
https://solarteameindhoven.nl/


I'd characterize it as a problem that can't be solved with traditional 
old solutions (heavy steel cars, etc.) But it can be solved with new 
technology, as has been demonstrated many times by solar cars. It just 
requires people to think outside the box.


Heck, batteries are good enough that you could even do it without the 
solar panels. Or even less...


"I've invented an amazing machine that can transport people over a 
hundred miles a day. It's clean, quiet, non-polluting, inexpensive, and 
uses no fossil fuels, motors, or batteries. I call it a 'bicycle'".


Lee Hart

--
If happiness is on your mind, here's a daily list to find:
 - something to do
 - something to look forward to
 - someone to love
 - someone to take good care of
 - and misbehave, just a little
 --
Lee Hart, 814 8th Ave N, Sartell MN 56377, www.sunrise-ev.com
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-11 Thread Lawrence Rhodes via EV
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Subject: Re: [EVDL] Solar powered vehicle panel requirements.
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It's a math problem that can't be solved. At least not with today's 
technology.
I think it is a weight problem that can be solved with today's technology...at 
least by students in Holland. Of course you can't do it with the piggy Tesla's 
and Bolts. Something much lighter. Lawrence Rhodes 
https://solarteameindhoven.nl/



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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-10 Thread Alan Arrison via EV
It's a math problem that can't be solved. At least not with today's 
technology.


On 7/10/2020 2:21 AM, Lawrence Rhodes via EV wrote:

The math problem here is consumption over time. A solar racer with a 5 
passenger capacity 850 pound weight with a coefficient of drag of .16  rolling 
on moped wheels with a 1.5kw panel and 15kw battery can attain 45mph 
continuously without using battery power. A Nissan Leaf going 55mph achieving 5 
miles per kwh would(if I got my math right) need 12kw continuously to keep that 
speed in full sunlight.  Of course the battery is a buffer that will allow you 
to do faster speeds and climb hills. I suspect some sort of Pop tent trailer 
might be a good combination for the Cyber Truck. 450.5 sq. ft. is the maximum 
size of a trailer. A pop tent that size would be quite a mansion. However that 
might only produce 5 to 6kw. Enough to charge and extend but not to run 
continuously.  Weight must be reduced and coefficient of drag lowered. It's a 
math problem.  Lawrence Rhodes
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-10 Thread Lawrence Rhodes via EV
 I commonly get much better range. My indicator of accumulated data says 4.9 
miles per kwh. Your mileage may vary. Lawrence Rhodes

On Friday, July 10, 2020, 9:50:10 AM PDT, Tom Mandera  
wrote:  
 
  
Assuming the 24kwh battery Leaf goes 80 miles, that's 3.3 miles / kwh or 
0.3kwh/mile or 300wh / mile.
 

 
 
80miles / 24kwh = 3.3 miles /kw or 1/3.3 kwh per mile.
 
 
Assuming a linear consumption (which is wrong - ignoring increased drag at 
speed, but convenient) that means at 55mph, traveling 1 hour, we need 16.5kwh 
of juice.
 

 
 
or 16,500w of solar to equal the consumption.
 

 
 
So the 12kw figure was on the low side, even assuming a linear consumption.
 

 
 
Unless I fouled up the math again. :)
 
 

 
 
 On 7/10/20 8:07 AM, paul dove wrote:
  
  That math seems wrong to me. 3200 Wh at 25Wh/m = 12.8 miles not 1 mile.
  
  On Friday, July 10, 2020, 8:22:02 AM CDT, Tom Mandera via EV 
 wrote:  
  
   There are 400w panels out that are roughly 7'x3.5'  So a rather 
 reasonable 7'x7' trailer could produce 800w, which is a good amount of 
 power - but not nearly enough.
 
 Assuming they're mounted flat, that's 800w at high noon, and less at 
 every other part of the day.  We could expect something like 3.2kwh / 
 day of production, or roughly a 1 mile extension in range.
 
 To get the 12kw needed, we need at least 15 times that, or 105' long 
 trailer, 7' wide.  Then we could drive continuously at around the noon 
 hour for around an hour, on a good sunny day.
 
 
 Sadly, as you said, it's a math problem..
 
 On 7/10/20 12:21 AM, Lawrence Rhodes via EV wrote:
 > The math problem here is consumption over time. A solar racer with a 5 
 > passenger capacity 850 pound weight with a coefficient of drag of .16  
 > rolling on moped wheels with a 1.5kw panel and 15kw battery can attain 45mph 
 > continuously without using battery power. A Nissan Leaf going 55mph 
 > achieving 5 miles per kwh would(if I got my math right) need 12kw 
 > continuously to keep that speed in full sunlight.  Of course the battery is 
 > a buffer that will allow you to do faster speeds and climb hills. I suspect 
 > some sort of Pop tent trailer might be a good combination for the Cyber 
 > Truck. 450.5 sq. ft. is the maximum size of a trailer. A pop tent that size 
 > would be quite a mansion. However that might only produce 5 to 6kw. Enough 
 > to charge and extend but not to run continuously.  Weight must be reduced 
 > and coefficient of drag lowered. It's a math problem.  Lawrence Rhodes
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-10 Thread paul dove via EV
 That math seems wrong to me. 3200 Wh at 25Wh/m = 12.8 miles not 1 mile.

On Friday, July 10, 2020, 8:22:02 AM CDT, Tom Mandera via EV 
 wrote:  
 
 There are 400w panels out that are roughly 7'x3.5'  So a rather 
reasonable 7'x7' trailer could produce 800w, which is a good amount of 
power - but not nearly enough.

Assuming they're mounted flat, that's 800w at high noon, and less at 
every other part of the day.  We could expect something like 3.2kwh / 
day of production, or roughly a 1 mile extension in range.

To get the 12kw needed, we need at least 15 times that, or 105' long 
trailer, 7' wide.  Then we could drive continuously at around the noon 
hour for around an hour, on a good sunny day.


Sadly, as you said, it's a math problem..

On 7/10/20 12:21 AM, Lawrence Rhodes via EV wrote:
> The math problem here is consumption over time. A solar racer with a 5 
> passenger capacity 850 pound weight with a coefficient of drag of .16  
> rolling on moped wheels with a 1.5kw panel and 15kw battery can attain 45mph 
> continuously without using battery power. A Nissan Leaf going 55mph achieving 
> 5 miles per kwh would(if I got my math right) need 12kw continuously to keep 
> that speed in full sunlight.  Of course the battery is a buffer that will 
> allow you to do faster speeds and climb hills. I suspect some sort of Pop 
> tent trailer might be a good combination for the Cyber Truck. 450.5 sq. ft. 
> is the maximum size of a trailer. A pop tent that size would be quite a 
> mansion. However that might only produce 5 to 6kw. Enough to charge and 
> extend but not to run continuously.  Weight must be reduced and coefficient 
> of drag lowered. It's a math problem.  Lawrence Rhodes
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Re: [EVDL] Solar powered vehicle panel requirements.

2020-07-10 Thread Tom Mandera via EV
There are 400w panels out that are roughly 7'x3.5'  So a rather 
reasonable 7'x7' trailer could produce 800w, which is a good amount of 
power - but not nearly enough.


Assuming they're mounted flat, that's 800w at high noon, and less at 
every other part of the day.  We could expect something like 3.2kwh / 
day of production, or roughly a 1 mile extension in range.


To get the 12kw needed, we need at least 15 times that, or 105' long 
trailer, 7' wide.  Then we could drive continuously at around the noon 
hour for around an hour, on a good sunny day.



Sadly, as you said, it's a math problem..

On 7/10/20 12:21 AM, Lawrence Rhodes via EV wrote:

The math problem here is consumption over time. A solar racer with a 5 
passenger capacity 850 pound weight with a coefficient of drag of .16  rolling 
on moped wheels with a 1.5kw panel and 15kw battery can attain 45mph 
continuously without using battery power. A Nissan Leaf going 55mph achieving 5 
miles per kwh would(if I got my math right) need 12kw continuously to keep that 
speed in full sunlight.  Of course the battery is a buffer that will allow you 
to do faster speeds and climb hills. I suspect some sort of Pop tent trailer 
might be a good combination for the Cyber Truck. 450.5 sq. ft. is the maximum 
size of a trailer. A pop tent that size would be quite a mansion. However that 
might only produce 5 to 6kw. Enough to charge and extend but not to run 
continuously.  Weight must be reduced and coefficient of drag lowered. It's a 
math problem.  Lawrence Rhodes
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