Surely two planes with the same weight and same Vs and same HP (thrust) must climb at the same vertical speed.
Excess power is what makes a plane climb. Induced + parasite drag combined is what uses power when level, so it seems to me that if induced drag is reduced by less wing tip losses (resulting from higher aspect ratio), the plane will have more excess power available for climb.
At such low speeds, aerodynamics won't be a first order factor.
It's surprisingly important. I fly gliders too. I have an old Schliecher Ka-8. When you go between thermals, you want to pass through the sink quickly so you fly "fast" - where the definition of "fast" is only about 50 or 60 knots, slower than the climb speed of an Arrow or a DA-40. If you go 60 knots in the Ka-8 the descent rate becomes very high because you're burning so much energy in overcoming a fairly draggy airframe. If I do the same in a fibreglass glider that weighs the same I may lose less than a third of the height in the same situation at the same speed because I'm burning so much less energy in overcoming drag. The difference is striking.
Similarly, compare (say) a Europa two-up with the 100hp Rotax 912S engine and a Cessna 150 with a 100hp O-200 one up (the Vs of these aircraft is only about a knot apart). At that loading both will weigh about the same, and both have similar climb out speeds. Go fly on a "standard atmosphere" day. You'll be lucky to get 800 fpm climb in the 150, but the Europa will be climbing at somewhere between 1600 and 1800 fpm at the same speed. That difference just isn't accounted for by the Europa having a better prop.
I would think the main factor in addition to having a VP prop is likely to be weight.
Europa - empty weight around 350kg C150/152 - empty weight around 500kg.
And I'll take that 800fpm Cessna, I'm lucky if I can get 600fpm out of the knackered things I have to teach in...
Europa - empty weight around 350kg
C150/152 - empty weight around 500kg.
How long do you think a Europa would last in a typical school?
12 months?
I had a go in the Europa derivative Liberty XL2 once, and although it flew well enough I wasn't as impressed as I thought I'd be.
Anyone have any experience with the XL2? Are they still in business?
I would think the main factor in addition to having a VP prop is likely to be weight.
That's why I specified the Europa be two up and the C150 one up, so their weights are approximately the same for comparison. I've flown the Europa tri-gear two up plenty of times, and also (a really, really nice - as in looks like it just came from the factory nice) Cessna 150 solo plenty of times, so I have a base to compare. The Europa's performance at the same weight climb performance at the same actual weight as the C150 is massively better, showing aerodynamics is pretty important even at climb speed.
That's not to deny the C150 is a better plane to put into a flight school. But that wasn't the proposition here, we're just interested if aerodynamics affects climb performance - which we find it does (and significantly).
If we want to see where the energy is going, consider this. 100hp is 74570 watts (74570 joules per second). The specifications for a C150 says it should climb at 3.4m/s at a weight of 730kg. One joule is the energy required to lift 0.1kg through 1 meter. So 74570 joules per second, in a drag-free environment, should lift 730kg at a speed of 10.2m/s. Since we're going up at only 3.4m/s that means only 24820 joules per second are going into making us climb, and we're losing 49750 joules per second to other things - propeller inefficiency, drag, etc. and I hypothesise that most of this 49750 watts of power* is going into overcoming airframe drag (induced and form drag). The Europa case would suggest that this be true, given that a C150 loaded to be the same weight as a Europa climbs dramatically less quickly.
A Cessna 150 does not have 100 HP avaiable at Vy because it doesn't have a variable pitch propeller. The Europa may or may not have a variable pitch propeller, depending on the specific aircraft.
Fixed pitch metal props have good energy efficiency, but by their design they don't let the engine produce full power, or burn the fuel associated with full power, in all phases of flight.
An interesting calculation.
Are the two types matched in Vs (wing loading) and are they climbing at the same speed i.e. on the same part of the drag curve?
The average consumption of a house with a family living in it in the UK is about 650W
That is suprisingly low. I have a wattmeter in our house and ours is about 3x that. And we are oil heated, and very well insulated.
But yes engines (vehicles) are very wasteful. A small car doing 70mph is probably working at ~30HP i.e. ~20kW.
The cost of any travelling is very high, and is suprisingly constant regardless of the method. A 747 burns about the same fuel per 4 people as you would burn driving a car with 4 people the same distance. It makes it seem effortless but that's because the stuff is neatly hidden in the wings and just vanishes into the air 
According to a recent Boeing advert I saw, the new 787 burns only 20% less fuel than a TB20, per passenger. Of course you get more cabin crew in a 787, though you might get a more attractive kind of "cabin crew" in a TB20 
How long do you think a Europa would last in a typical school? 12 months?
I know of a really busy school using Tecnams and some of them have now more than 4000h. The often mentioned 'fragility' of these light aircraft seems to be more of a myth than a reality.
