All I ask is why? Would it be a good idea to put a flat plate behind the propeller of an airplane? No. “How are my ESCs going to stay cool if I don’t put them under the prop wash?!” Prop wash cooling is overkill.
As our quad increases in speed, so does the amount of drag force it encounters. Our quad will keep accelerating as long as the thrust force is greater than the drag force. Once these forces are equal, we stop accelerating and our velocity stays the same. When it comes to velocity, we can see that our thrust is being used up in 2 different ways:
- Drag offset
Keep in mind that our thrust decreases linearly with speed up to the theoretical pitch speed. To reach pitch speed, we have a thrust of 0 meaning we would have to eliminate drag completely (which will never happen). If we want to go faster, we need to have more of the thrust go towards acceleration and less soaked up in drag. How to do this? Take a look at the drag equation:
Fd = ½ ρ Cd A v²
- Fd is drag force in Newtons
- ρ is the density of air in kg/m³
- Cd is the drag coefficient
- A is the cross section of our quad in m³ in the direction of movement
- v is the velocity in m/s
The only two variables we have direct control over is A and Cd. The main thing to keep in mind here (mathematically) is that the v is squared. That means that if we cut our A or Cd in half, our overall Fd will only be cut by ¼. Not only that, we will have an increase in velocity which means Fd won’t even be cut by ¼. However, since frame designs are so poorly designed for aerodynamics, we can easily gain a significant amount of speed by reducing our area and streamlining the frame.
A note on the calculations: since there are multiple variables that are dependent on one another, calculations are carried out using differential equations/calculus and not easily done by hand. I do have a spreadsheet that I would like to embed and hopefully will be able to soon. Also – these calculations can only get us in the ballpark. Empirical modeling can get us closer, but it is beyond any equipment that I have at my disposal.
Effects of reducing A and Cd
We’ll take a look at a 500g quad running a 4s with 4.5 pitch props, 4.8kg total thrust, 2300kv motors, a top view area of 12,000mm², a front view area of 4000mm², and a Cd of 1.6. Calculating it out, this would have a top speed of around 84mph which is typical. Below you can see the effect of area reduction and streamlining:
- 95mph by reducing Cd to 1.0
- 102mph by reducing Cd to 0.7
- 104mph by reducing Cd to 0.7 and reducing A by 10%
- 107mph by reducing Cd to 0.7 and reducing A by 25%
We gained an extra 18mph from reducing Cd and an extra 5mph from reducing area. It is much easier to reduce Cd than it is to reduce area.
Cd can be reduced in a number of ways. Since quads are such an unusual design in terms of conventional air born objects, it is not a straight forward process. Way to reduce Cd:
- Rounding our sharp edges
- Eliminating places where air can get “pocketed”
- Making sure surfaces are smooth
- Eliminating any surfaces that act like air brakes.
Round motor arms
Not only do they reduce surface area, but they also reduce Cd. Essentially, you can get rid of 4 air brakes on your quad.
Reducing area isn’t as clear cut as it seems. This is because we are only concerned with the projected cross section that is perpendicular to the direction of movement. This projected cross section is constantly changing as we change speed and/or pitch. I will illustrate this concept in the next section which also points out one of the biggest design issues in today’s quad frames.