How fast does our six foot (2 m) Piper Cub needs to fly and land? Piece of cake!
In this series I use a six foot (2 m) scale model of a Piper Cub as an example for performing various simple calculations useful for model airplanes. This is the third article in the series. Here’s a link to the other articles:
Spreadsheet with Calculations
You can download a spreadsheet with all the calculations in this article in both U.S. customary and metric units of measure by clicking here.
To do our calculations, all we need is the most basic specifications of our Piper Cub model that we calculated in the first article of the series. I’m talking about the wing span, wing area, and total flying weight. In the spreadsheet, these cells have a green background color.
The even better news is that this is the core set of numbers that you can expect to find in just about every model airplane product catalog or plan. That makes it very easy to compute these flying speeds for a kit you are thinking about buying, for example.
There’s a minimal set of assumptions that we need to make to compute the results. You can modify these values, but in most cases the values I provided will work fine. These cells in the spreadsheet have an orange background color.
First, we need to estimate the minimum drag coefficient of the entire airplane. There are many factors that go into this number. The lower the value, the less draggy the airplane. Coefficients are dimensionless, which means that they are not related to the airplane size.
Different wings can generate different amounts of maximum lift before they stall. This depends mainly on the airfoil used and the wing shape. This maximum lift generation factor is called the maximum lift coefficient. The typical range for an unflapped wing is 1.0 to 1.5. In our case, I’m assuming a flat bottomed (“Clark Y”) airfoil and no flaps.
The air density accounts for the altitude. The spreadsheet assumes sea level.
As a bonus, the spreadsheet also calculates the minimum turning radius at the various speeds. The bank angle is how much the wing will be banked when doing these turns. Forty-five degrees is a good value for this.
The next block of values in the spreadsheet, colored red, are intermediate results that should not be changed. The first two, earth gravity and wing aspect ratio, should be self-explanatory.
The final value in this section, best L/D lift coefficient, is computed from the minimum drag coefficient and the wing aspect ratio. This is the lift coefficient value at which the wing is most efficient. There should not be any need to change this computed value.
There’s a simple formula that computes the required flying speed for an airplane to stay up given its wing area, flying weight, altitude, and current lift coefficient. Most of these values are constants for a given airplane. If we plug in the maximum lift coefficient into the formula, then it will compute the stall speed of the airplane.
The stall speed is a major factor in determining the take-off roll distance and the landing distance. These, in turn, are an indication of how much of a handful it will be to take-off and land this airplane.
Looking at the factors that go into the equation, the primary means to lower the stall speed is to lower the wing loading. In other words, either make the wing larger or decrease the flying weight.
The recommended landing speed is just a prudent margin above the stall speed. Normally it is 1.3 times the stall speed. As an additional safety margin, add half the wind gust speed to the value. So if there are gusts of ten miles per hour, add five mph to the landing speed.
Maximum Range Speed
The speed at which the wing is most efficient is the maximum range speed. More technically, this is the speed where the lift to drag ratio is highest. This is a good speed to know, but in practice we usually fly faster than this when we are cruising our model airplanes around.
For most wings, their most efficient lift coefficient is around 0.4. To compute the maximum range speed, we use the same formula we used to compute the stalling speed. Instead of plugging in the maximum lift coefficient, we plug in the lift coefficient for best efficiency.
Maximum Endurance Speed
The maximum endurance speed is the speed were we get to fly around for the longest. It is also called the minimum sink rate speed. Computing this value is easy. We just need to divide the maximum range speed by 1.32, or the fourth root of three. Why? Well, just take my word for it.
For a model airplane that’s just flying around, you could argue that this is the best speed to fly at. It’s not like we need to get anywhere. But there are problems with that logic. First, we would be flying very close to the stall speed. That is just looking for trouble. Second, the airplane would be flying very nose high, which just does not look right. Third, we would not have any excess energy to do any kind of maneuvers.
When flying a glider, this is the speed at which we need to thermal. The turning radius at this speed becomes a critical performance number. The smaller the turning radius, the smaller a thermal we can use to advantage. Again, being in a bumpy thermal so close to the stall speed is a bad idea, so being a bit faster than this would be prudent.
But at what speed should we be flying at if we are actually trying to get somewhere and we care about efficiency? That is the so-called “best-speed” speed. Similar to the maximum endurance speed, it is the maximum range speed times the fourth root of three (about 1.32).
Also called the Carson speed after its discoverer, this is the speed to use when you care equally about efficiency and about getting there quickly.
Piper Cub Results
I have colored yellow the most useful results from the spreadsheet. We can see that we need to land at about 20 mph (32 kph) and cruise around at between 30 to 40 mph (48 to 65 kph). We are looking at about a 50 foot (15 m) turning radius.