As I mentioned in my previous post, Sergio, belt length, wrap angle, pulley size, and drive ratio have no significant effect on power transmission. It is possible to have a power transmission so poorly designed that it would suffer from lower efficiency, but you won't find such a situation on any modern woodturning lathe. The motor to spindle efficiency on any woodturning lathe that uses J-section belts will be within the range of 96 to 99%. Older design lathes that use A-section belts will probably have an efficiency in the range of 85 to 90%. Lathes that use a jack shaft will have a much lower efficiency in the vicinity of 75%.
Power transmission efficiency is not a simple fixed constant, but varies a few percent under various operating conditions. Most of those conditions have a very small effect on efficiency, but operation outside the design envelope can result in a much greater reduction in efficiency. One of the most common offenders in lowering efficiency is excessive belt tension. For example, increasing tension from 50 pounds to 150 pounds can result in a 50 to 100% idling power loss. High RPM's (for example 3600 RPM vs. 1800 RPM) also can result in power loss that is comparable to high belt tension power loss. Small diameter pulleys are also a cause of greater power loss. Minimum pulley size is a function of the type belt being used and the maximum speed of the pulley (because flexing the belt beyond a certain amount results in energy this is not recovered when the belt unwraps from the pulley and velocity is important because it determines how fast the belt is flexing as it wraps and unwraps around the pulley). There is also a maximum belt speed measure in feet per minute for each type of belt and operation above that speed can produce a drastic reduction in efficiency because of the increase in friction. The physics behind that characteristic has to do with the aerodynamic forces due to pressure and vacuum created as the belt wraps and unwraps from the pulley. At this point, you can probably see that there are some conflicting design parameters in different parts of the operating envelope. For instance, a too small diameter pulley reduces efficiency, but a large diameter pulley will cause the belt to have a higher linear velocity. So, at the high speed portion of the operating envelope there is a resulting design trade-off between belt speed and pulley size.
From your previous posts, I can see that your main concern is related to the belt wrap angle (what you described as belt length). The effect of wrap angle is generally insignificant except for very extreme cases. The wrap angle can be too large as well as too small. As a rough guideline try to not have wrap angles greater than 225° or less than 120°. These are not hard and fast limits, but a good rule of thumb. You cite friction as a benefit of greater contact area, but in actuality friction is a parasitic power loss. Also, friction is not very dependent upon contact area. Other factors such as tension and speed have a greater effect on friction losses.
This is getting somewhat lengthy, but I may continue on later in other factors that have greater bearing on mechanical output power. But, suffice it to say that for an efficient belt drive power transmission (which would be the case for all of the upper end woodturning lathes), the power available at the spindle is essentially the same as the power at the motor shaft. Pulley size ratio and all of the other variables mentioned have no significant effect on efficiency. Just assume that the worst-case condition within the operating envelope of any of these Poly-V driven variable speed lathes is no worse than 95% and you'll be close to dead-on.
BTW, Oz is Internet slang for Australia in case you misunderstood my previous comment. I still think that it would be a good idea to go there and get a Vicmarc chuck straight from the source. Only problem might be that their 1¼X8 chuck might be an an export-only model. 😀
