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Will I be able to charge my roadster?

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He said Tesla HQ (Palo Alto)

PA HQ has outside EVSEs for visitors:

Not sure what their policy would be with regards to someone using them after hours.

I've charged there. I recall a gate across the entrance, and Google Maps seems to confirm that.

I am quite sure they would be happy to arrange to have the gate open for a one-time event, but doubt they'd want to allow after-hours access on a regular basis. But Calif mentioned leaving it overnight...if you can get it in and out during regular hours, that might work if they don't regularly have cars there (I wouldn't think they would have them overnight at this location, but you never know). Of course you'd have to check with them, and lack of reply is why you asked here...sorry.
 
Based on upon my experience I get 30 - 32 Ideal Miles per hour at 40amps and my one time experience at 70 amps I got ~52 Ideal Miles per hour.

Sounds about right. Charging mileage may vary due to ambient temperature (more cooling power required if hot), and also how much voltage (around here we get 208V if from commercial 3-phase source, 240V if residential 2-phase).
 
FWIW I've plugged into 120v 12A using a 50 foot extension cord (very heavy gauge) without issue.

Again, for what it's worth, I'm charging this week while on vacation using the same 50 foot cord (12 gauge) connected to another 25 foot cord (12 gauge) for a total of 75 feet. No issues. The circuits where I'm at are a bit weak -- the voltage drop is 121 -> 111 while charging (12 amps). Takes a damn long time to charge, but it's fine for recovering from the trip to get here and topping off any local driving activity. Cord and connections get no more than luke-warm.

I did have a very difficult time securing a way to charge here. I was plugged into an outside box on just the 50 foot cord for about 30 hours before tripping the breaker. Long story short, that outside outlet is shared with the bathrooms of the unit (this is a timeshare complex)! And it's not our unit. So hairdryer + charging = oops. My 50 footer didn't reach any other location on site that they could figure out .. .until they realized a couple units were unoccupied. So I tried those. One unit's outlet was dead (and the guy already left). The other one was to weak to support 12 amps -- as the Roadster ramped up the amps (seen on the VDS), the voltage quickly dropped and resulted in a charging error.

Then I started hunting around for public stations. There's nothing here. And the J1772 at the Toyota is inside the service bay so not terribly convenient obviously.

Then I said what they hey, try adding another 25 foot cord and run the line to OUR outside 120v outlet ... and I'm good to go.

I almost didn't bring other charging cords figuring I'd have no problem with 120v (I've been here before, charged all week from that first outlet without issue). Very glad I decided NOT to do that. Gives me options ... never know what you're going to run in to.