Nov 3, 2013

Disk Loading and Solidity: The Math Behind “The Feel”

Ok, so you’ve heard the terminology before, but you never quite understood why someone would be using the phrase “disk loading” in relation to their heli, right? There is a reason, trust me… Let’s start with the basics…the math, that is! ūüėȬ†Disk loading is an easy calculation to perform. What you need to do first is to get some measurements:

 

1. Center-to-bolt length on the head (head radius in millimeters, Rh)

2. Bolt-to-tip length on the blade (blade length in millimeters, Lb)

3. All-up weight of your heli (weight fully loaded and ready to fly in kilograms, W…kilograms = pounds / 2.2)

 

Now, the calculation can be performed:

DL = W / [Pi * (Rh/1000 + Lb/1000)^2] is disk loading in kilograms per square meter

 

What does this mean though? Well, this is a performance parameter that allows designers and pilots to judge the relative agility and feel of the heli during flight as well as its susceptibility to wind. The general trend is as follows:

Low DL ‚Äď Usually described as “floaty” or “like a feather” in that it seems to hang in certain maneuvers. Can be “boggy” if not treated with care.¬†Will get “blown around” by wind.¬†Very snappy under power, but sensitive to small errors in stick commands. As a result, these helis are not as easy to fly “in a box” as in hardcore smack flying on the deck. They tend to be more suited to big air/smooth 3D and excel at autorotations due to the higher lift.

High DL ‚Äď Feels “heavy” in the air and lacks hang time, but also feels more controlled during high-agility maneuvers. Tends to feel like it has a lot of inertia coming out of maneuvers, which gives it less sensitivity to small errors in stick commands. These helis are best at “box” flying and throwing down. Because they’re not floaty and touchy, they can be corralled into a much smaller area, but are poorer at autorotations due to their lower potential lift for the same sink rate.

The disclaimer on all of this is that it’s a very personal thing‚Ķkind of like how people feel about blades!¬†:)¬†Remember that there are all sorts of people out there flying both of these extremes and everything in between for anything from sport flight up to full-on extreme deck-smack.¬†For instance, I fly big air 3D and prefer a higher DL heli nowadays, but when I first got started, I really enjoyed a low DL because of the hang time that it gave me to get through maneuvers.

Ok, so that’s the whole story, right? Wrong! You’ve got a way to calculate the relative feel of the heli overall, but what if you want to get a measure of the relative feel when power is applied or determine how to get the same “pull” out of a heli with two different types of blades by simply varying your collective pitch range?

Enter rotor solidity‚ĶSolidity is simply how much of the total disk area is made up of blades. So let’s calculate it. First, you’re going to need to dig up the values of Lb and Rh from above. Then, you’re going to need the chord length of the blade or the blades width, Lc and the number of blades on the heli, Nb. To calculate the solidity, you take the area covered by blades and divide it by the area of the disk like this:

 

S = [Nb * Lc * Lb] / [Pi * (Rh + Lb)^2]

 

A higher solidity will give you a much more abrupt power delivery and snappy response from the same collective pitch range and head speed, but can be much more “boggy” and will draw more power for the same flight (less efficient). A lower solidity will give a smoother sometimes even delayed power delivery from the same collective pitch range and head speed, but will not bog as readily and is less power hungry (more efficient).¬†Not surprisingly, a higher solidity seems to have a lot in common with a lower DL. Why? Because it’s all about comparing blade area and how that affects the heli’s performance and behavior.

Generally speaking, full-scale heli designers seek to minimize solidity in order to reduce rotor mass and thus stresses on the system, but you can’t go too far or else you’ll have to increase your collective pitch so much that the blades will stall, so there’s a limit to everything‚Ķ Luckily, we’re not so worried about these issues the RC heli hobby‚Ķ Ok, so do you want to know what pitch you should run on a new set of 59mm-chord 710’s when you’ve been running 12 degrees on a set of 63mm-chord 690’s?

 

P_new = P_old * (S_old / S_new ) ‚Ķ this formula isn’t perfect and makes certain assumptions, but it’s a good starting point to get you moving in the right direction.

 

Solidity isn’t something that most people know about let alone employ in RC heli calculations, but in full-scale heli design, it’s a serious thing. It really has more to do with how efficient the rotor system will be, as an increase in solidity increases parasitic drag (skin friction-based drag) and thus a heli with higher solidity will require more power to maintain a hover, for example.

Disk loading is really only the weight of the heli divided by the apparent diameter of the rotor. It gives you a feel for how different helis or different rotors will perform in a relative sense, but it’s not the whole picture‚Ķ Solidity, on the other hand, will give you what can be referred to as blade loading when you divide it into the disk loading value.

Why is solidity so important? Well, let’s do some math.¬†;)¬†We’ll compare two equal-length blades with different chords to two equal-chord blades with different lengths. For simplicity we’ll assume that the head has no length to it (blades are connected magically at their roots) and the heli is 11 pounds (5kg).

 

Radix 690FBLV2: 690mm/64mm

Align 6903D: 690mm/60mm

Radix 710FBLV2: 710mm/64mm

 

Here goes…

TechTip_DiskLoading_758x71

 

Notice how DL doesn’t tell the entire story? Those two sets of 690’s have the same disk loading, but they’re not going to feel the same in the air. Also, notice that for the same chord, the blade length plays a less significant role on the blade loading than does the different chords on the same blade length.

I use solidity in my calculations when I consider different heli setups for this reason. Is it necessary? Nope. Most people just deal in simpler terms: length and chord, but this gives me a better way to compare configurations in a relative sense. It just depends on how nerdy you want to get…

– Justin