Let's see if I can thoroughly confuse everyone. To get an idea of why the air velocity varies with vane shape, consider flatbed truck going down the highway at 100 mph. On the bed of the truck is a baseball pitcher and an observer. There is also an observer on the ground watching the truck as it passes. There is no wind resistance.
Case 1. The pitcher fires a fastball at 100 mph in the direction the truck is going and at an angle to the horizontal of 30 degrees. To the observer on the truck the ball appears to travel at 100 mph at an angle of 30 degrees. To the observer on the ground, because he sees not only the ball moving, but also the truck, the ball appears to be moving at 193 mph at an angle of 15 degrees. This is because of the vector sums of the two velocities. This corresponds to a forward curved blade fan. The speed of the truck is the wheel velocity and thrown ball is the velocity of the the air leaving the tip of the blade.
Case 2. The pitcher turns around and throws in a direction opposite the direction of the truck otherwise same as before. Again to the observer on the truck sees the ball appear to be thrown at 100 mph at an angle of 30 degrees. To the observer on the ground, the velocity appears to be only 52 mph at an angle of 75 degrees to the horizontal (almost straight up!). This is the backward curved blade.
Seems strange but that is way vectors work.
The air leaving the edge of the blade always leaves in the a direction tangent to the blade tip. The wheel tip velocity is the product of the wheel rotation speed and the radius.
Confused?
Tom