Hill-climbing
From Apterawiki
Since the data is not yet public, precise figures for hill-climbing performance is not yet available. This page will cover the issues related to hill climbing from a physics standpoint until such data becomes available.
[edit] Issue #1: Range
Climbing a hill involves moving from a lower gravitational potential energy state to a higher one, which inherently consumes energy. If we assume the mass of a loaded Aptera is 900 kilograms (base weight + 500lbs), then by U=mgh, the potential energy change is 8829J/m, which is about 0.75 watt hours per foot of climb. As the Aptera's battery pack holds 10kWh, every thousand feet of climbing should consume about 7.5% of the battery pack. This is about nine miles of range lost per thousand feet at 55mph or five miles at 80mph. Factoring in drivetrain losses, these numbers would probably be closer to ten miles and six miles, respectively.
A number of factors can affect your actual range over mountains. Any reduction in your speed increases your range, so if the road leads to you travelling slower, the loss of range could be lower. Any additional cornering or stop/start driving, however, will impose additional penalties to your range.
[edit] Issue #2: Performance
While not explicitly stated, there is absolutely no reason to suspect that the lithium phosphate batteries (famed for their power density) cannot provide the maximum power for the (rather small) 30kW motor[1], given their power density of about 3kW/kg.[2]. Given that the reported 70 mile range at 80mph implies a consumption of 11.4kW, this means that almost a two thirds of the vehicle's power -- 18.6kW -- is still available at that speed. That's 66.9 MJ per hour. Assuming a mass of 900kg fully loaded (as above), this implies the ability to climb 7,600 meters per hour. After drivetrain losses, it's probably closer to 7,000 meters (4.4 miles). This equates to a roughly 5 1/2 percent grade. If you repeat the calculations for driving at 55mph, it comes out to almost six miles height per hour and a maximum grade of roughly 10 1/2%. The slower the vehicle goes, the steeper the grade it can climb, since the total energy requirements of the change in altitude are spread out over a greater period of time. The maximum permissable grade for an interstate in a mountainous area is 6%[3]. This implies that an Aptera would be able to drive the steepest interstates at just under 80mph.
Another situation to consider is the Typ-1h when going beyond the range of its battery pack. The Typ-1h's generator produces 12kW[4]. As we can see in the above calculation, at 80mph, the Typ-1h's generator should be considered almost completely taxed on flat land, and only able to climb small hills (0.6kW of power available to the climb) if its pack was completely discharged. In practice, of course, one can expect the vehicle to retain some amount of reserve charge for things like hills, but we'll want to consider the worst case. The question then arises, of course, at what speed could one climb hills? At 55mph, using 83Wh/mi, the Typ-1h would use 4.6kW on level ground, leaving 7.4kW for hill climbing. This equates to almost 3000 meters after drivetrain losses (almost 9,000 feet) per hour, certainly not a limit in any ordinary circumstance. Hence, the practical climbing limitation speed limitation in the Typ-1h with a discharged battery would fall somewhere between these figures. In practice, one would expect perhaps a kilowatt hour or so to be kept in reserve in the battery wherever possible for these contingencies.
Note that as the Typ-1h is a serial hybrid, the limits of the Typ-1h generator do not impose a limit on grades climbed, only on the average climb over a long period of time. Only the limitations of the 30kW motor impose limits on grades climbed.
