So what does the propeller thrust mean in terms of speed? Not much. Although we need thrust for movement, thrust will never be able to push us past our theoretical top speed (as calculated in Part 1). We will take a look at an example and see how thrust changes as the quad gets closer to its theoretical top speed. Then we will see what doubling the thrust will do.
All thrust tests are done on a static (or stationary) motor. Once a propeller is in a dynamic (moving) situation, the thrust changes. Putting the throttle to 100% and starting from 0 mph, the prop will be at maximum thrust. Thrust is generated from a propeller due to the pressure difference between the front and the rear of the prop. As the prop rotates, the underside of the blade compresses and pushes the air which creates a high pressure area. The topside of the prop, as it rotates, creates a low pressure area since air is “rushing” in to fill up the space the prop once occupied. This pressure difference is greatest when the quad is at a standstill since the pressure difference created is related to the velocity of the incoming air.
We Always Lose Thrust
Now comes the weird part: once our quad reaches top speed, the net thrust goes to 0 (in reality, we are still generating some thrust to offset drag). Here are a couple of examples to illustrate this:
The paddle boat
Think of being in a foot powered paddle boat. We will neglect all drag forces – the only force to overcome is acceleration. Your legs can put out 100kg of force, your maximum pedaling rate (RPM) is 100 and the paddle moves at 20 mph at this RPM. When you start pedaling from 0 mph, you are exerting your full 100kg of force – you are putting out your maximum force since you are pushing against the (relatively) stationary water. As you gain speed, it becomes easier and easier the closer you get to your maximum pedaling rate. This is because the water coming at the paddle (relative to the boat) is getting closer and closer to your max paddle speed. And because there is a difference in speed between the paddle and the medium (water) you are paddling against, you keep accelerating. Once the incoming water reaches the paddle speed, you are no longer accelerating. Neglecting friction, the force needed from your legs to keep this speed is 0kg.
This time, think of a scooter that you propel with your foot pushing against the ground. Think of your shoe as the prop and the ground being the air pushed by the prop. We’ll say you can swing your leg at a maximum speed of 20mph. When starting off on the scooter, the ground you are pushing against is at 0mph and this is where you feel the greatest resistance and therefore have to put out your maximum amount of effort (thrust). When the scooter is at 20mph and you try pushing faster, you are unable to since the ground you are pushing against is now travelling at 20mph (relative to you) and you cannot create a difference in pressure between your foot and the ground. Your thrust is basically 0. The little effort you need to put in is used to maintain speed since some speed is lost through air drag (and in this case, wheel friction, etc.).
These same principles can be applied to propellers on quads. In theory, thrust will drop linearly with speed and our thrust will be at 0g at top speed since the medium (air) that we are pushing against matches our prop speed.
In our real world, we find out that it still takes 20kg of force keep paddling at 100 RPM. That means only 80kg of your legs 100kg of force is translated into speed and the other 20kg is soaked up by drag forces. To be more specific, 80kg went towards generating impulse which correlates to acceleration – speed only increases as long as we can keep accelerating. In theory, this should be proportional to speed. Since 80% of our force has gone into our speed: .80 × 20mph = 16mph.
This also applies to the quads. Since thrust diminishes with speed, we will never reach our theoretical speed since we still need some thrust to offset air drag.
What if the person can exert twice the amount of force? Remember that RPM, paddle speed, and drag forces stay the same. Keeping the RPM speed at 20mph but with 200kg of force, we have 180kg being used as thrust which works out to be 90%. To find speed at this thrust: .90 × 20mph = 18mph. However, coming back to reality, we will be experiencing more drag since drag forces increase exponentially with speed. Without getting into the math (yet) and oversimplifying, 20kg of drag at 16mph will increase to 25.3kg of drag at 18mph. Now only 174.7kg is going to thrust which works out to be 87.4%: .874 × 20mph = 17.5mph (yes we could recalculate again, or better yet, use differential equations – but we will keep it simple). With a 100% increase in thrust, we only get a 9.4% increase in speed.
Why So Little?
The reasons are many, but it all boils down to the fact that when it comes to speed, thrust can only help to overcome drag forces, which at these speeds, is actually pretty significant (approximately 1.5kg for a typical 250 sized quad going 90mph).
Yes, This is Confusing…
If the drag forces (air resistance) is significant, how can thrust be insignificant in terms of speed? This is due to the fact that:
- The drag force increases exponentially with speed (it is squared)
- Doubling thrust doesn’t double the amount of drag we can overcome since thrust drops linearly with speed up to the theoretical pitch speed.
If you keep reading on this series, you’ll see the thrust equation and begin to understand the complex relationship and dependencies between all these factors. In fact, you can actually increase the effect thrust has on your quads speed by reducing its drag coefficient (Cd) by streamlining the frame. Yes, it’s a tangled web.
Update January 25, 2017: I’ve added a link to a spreadsheet on this page here (please read a little before using it) which is a great way to see the effect of thrust, prop pitch, frame area, RPM, etc.
Blade Number and Diameter
In terms of speed, it really comes down to the pitch. In my experience, more blades and larger diameter props are actually slower. I’m assuming this is due to the increased torque induced on the motor since there is an increase in the prop surface area being pushed though the air. This higher torque increases amp draw which causes voltage drop and less RPM’s. However, if the battery can handle it, larger diameter props/more blades typically put out more thrust and this can equate to quicker acceleration.
The deeper we look, the more we see how many intangible and complicated factors there are. My initial thought is to try out a 4045 prop on a 2600kv motor. Theoretically it should be faster since it can hit higher RPM’s. And if not, why? Why not put a 5045 on a 2600kv? My initial thought is that the voltage drop would be too much and there would be no advantage in RPM. I have not looked through all the data yet, but a great place to get some numbers regarding motor and propeller tests is at Mini Quad Test Bench.
Thrust Still Matters
More thrust provides better acceleration, or to be more specific, it provides greater impulse. In the next part of this series, I will go into more detail about the forces acting on the quad during flight including the relationship between thrust, gravity, pitch angle and speed.