Success...
Ok,
Just hooked up my variable power supply to the bike, and was able to run it up to 36/38 volts without any problem. See attached photos. All I did was connect the supply to the terminals , lift the rear tire and throttle it up. The meter in the picture is showing no amps as I couldn't operate both the camera and experiment at the same time.
The initial throttle pegged the amp meter, then backed down and showed a steady 2.5a load at full throttle. Oh course, not much load with it freewheeling, but I am now confident that the Ping 36v LifePo4 will work.
Jeff
You need to test under load, and if precisely metering voltage input to controller, you need to set it at ~43V,
not 36V. This is because a lithium battery (of any type) rated at 36V actually runs in a
range of voltage from just over 42V when fully charged, down to ~30V when "fully" discharged. This is inherent to how stored direct current outflow functions regardless of battery type.
There are a few differences to consider by battery type, such as C-rate, which is how quickly a battery can discharge (deliver power). Lithium batteries such as RC LiPo have C-rates allowing enormous release of power, and they get really hot. They're fun to watch burn, very dangerous, hard to extinguish. Next in C-rate comes the LiCo/Mn (also nickel, usually) which have a fairly fast discharge rate, but less than the volatile RC LiPo. These are your 18650 cylindrical batteries and equivalent. C-rate is high enough to more than deliver what you need. These batts also get hot, but don't as easily ignite like the RC's do. Finally, the (prismatic or cylindrical) LiFePO4 have the slowest C-rate, which is still much faster than ANY SLA or NiCad or NMH batteries can deliver. LiFePO4 are almost impossible to ignite, even when crushed (but don't try it).
My point about C-rate. If you're very quickly delivering ~43V into a controller rated for 24V (which actually means ~33V estimated max for rating purposes, since that's what a 24V battery delivers when fully charged), you're over-volting by ~30% to the controller, then it's over-volting however much additionally to the battery -- about the same 30% assuming the controller doesn't have circuitry to monitor, regulate, and step-down limit voltage output to motor. You're gonna heat up your controller, then you're gonna (maybe) heat up your motor, depending on the wattage the motor can truly handle (ratings mean nothing with these Currie motors, I've found).
So you'll probably get it to work, and you'll feel the speed difference with the substantial additional voltage, PLUS, the fact you won't be slowed down by the choke-point of SLA batteries' C-rate: that's why your bike slows down after sustained throttle, but seems to recover after a "rest" period. That's your SLA bank running out of discharge capacity because it can only put out high wattage for short times.
36V nominal LiFePO4 batteries worked just fine for me in a similar Currie of similar vintage. I got rid of that clunky rack and badly shaped drop-in packs that lose contact at every bump. I used a regular rack and panniers for a pair of 15Ah 36V batteries, then wired up a switchbox (to the top tube) allowing me to run either battery, or both in parallel. (If in parallel, one must start with near-equal voltage in both batts, and the output was more than enough to do damage if I would have stayed on the throttle constantly, but it delivered a ton of wattage and gave impressive top speeds. (This was using the existing "24V" controller and motor. Motor casing could get pretty hot, approx 130F to the touch, but it had cooling fins and a breeze on it, and I never saw degradation.)
So, in my experience, yes, you can do this, and I'll bet that you blow your controller before your motor goes. At that point, either replace the controller with a 36V version, or pull off the motor and controller and whatever else, then put in a 36V front wheel hub motor that'll have its own proprietary throttle and PAS sensor and whatever else. The bikes are built like tanks (just like the motors), and not overly heavy sans SLA batts, making them decent to keep and play around with.
Have fun. But do test at ~43V, and do it under full throttle load going UP-hill (get that wattage waaaay UP), and make sure it still works. Preferably do it with a fast C-rate (high-wattage) source -- if you don't have a 36V lithium source to do it with, then rig up 6 fully-charged 12V SLA batts into dual banks (3S) that you will run in parallel (2P). That will give you enough power to know for sure. Oh, and let off the throttle frequently... (LOL)