Ever since the Design Team finished a draft of the fuselage a week or so ago, we’ve shifted our focus to verifying the safety and functionality of our design through a mathematical lens. When we initially sized the wing a few months ago, we just eyeballed the Clark Y airfoil plots and did some quick calculations on a whiteboard. This was enough to get us started in the right direction, but before we start spending a lot of money on parts, it’s important that we take a closer look at all our calculations. To start off, we calculated our cruise Reynolds number based on our initial calculations which called for a 5ft cord with a thickness of 7.014in and a cruise velocity of 50 knots. The Reynolds number describes how turbulent or laminar the flow of air around our airfoil will be. Based on the turbulence of the air, an airfoil can behave quite differently, so it’s critical that we determine the Reynolds number to get accurate results. Below is a graph showing the relationship between the angle of attack (alpha) and the lift coefficient of the airfoil (Cl) with each line representing a different Reynolds number. Though all plots represent configurations of the Clark Y airfoil, it’s clear that the Reynolds number plays a large part in their stall behavior, with some stalling cleanly (highest plot) and some stalling unpredictably (lowest plot).
With our Reynolds number determined, we could isolate a specific plot that would more accurately represent our airfoil. Since Airfoil Tools only supplies Xfoil predictions for set Reynolds numbers, we had to round ours to the closest value. By clicking the “details” link next to the plot, we accessed the exact Xfoil data. To know if our wing is properly sized and will generate sufficient lift, we examined the angle of attack and lift coefficient data. By plugging in our weight calculations, mission requirements, and wing reference area into the lift coefficient equation, we determined the minimum lift coefficient required to achieve a maximum stall speed of 24 knots (as specified in Part 103). Unfortunately, we realized the Clark Y airfoil would stall long before producing a sufficient lift coefficient to maintain level flight at 24 knots. This means that our minimum speed would be greater than 24 knots, which would compromise the certifiability of our aircraft. In other words, our wing was simply too small.
To increase the wing reference area, we could either extend the wingspan or extend the length of the chord. Extending the wingspan would increase the aspect ratio but would come at the cost of extending our heavy aluminum spars. Alternatively, we could increase the length of the chord which would decrease the aspect ratio and therefore increase lift induced drag. Since ultralights are inherently draggy airplanes, we decided to extend the chord to 6ft and save a little weight.
Our second round of calculations can be broken down into two categories: stall and cruise. According to AC 103-7 section 21, our stall speed must legally be no greater than 24 knots. We can make our cruise speed whatever we want below 55knots, but ideally, we’d like it to be the velocity at which the airfoil has the lowest zero-lift drag coefficient.
For our stall calculations, we plugged in our new airfoil thickness, stall velocity, and kinematic viscosity at 59°F (a rough temperature average for San Francisco Bay Area weather). This produced a Reynolds number of approximately 1.81 E^4. We then selected the Clark Y plot with a Ncrit value of 9 and a Reynolds number of 2.00 E^4. We scrolled down the Xfoil prediction data and determined that at an angle of attack between 11 and 11.25 degrees, the airfoil would produce a lift coefficient between 1.3494 and 1.3609.
We then resolved the lift coefficient equation with our stall parameters and got a required lift coefficient of 1.356 which falls right within the range taken from the Xfoil predictions! In short, this told us 2 key things:
- Our plane would stall at 11-11.25 degrees AOA
- A reference area of 192ft^2 is just large enough to support level flight at 24 knots
Knowing our stall lift coefficient, it was time to calculate our required cruise lift coefficient. When we initially wrote our aircraft mission, we decided on a cruise speed of 50 knots (5 knots below the maximum speed of 55 knots). Our plane likely won’t have much range due to its electric powertrain so we wanted to have a high speed to cover a lot of distance in a short time. Admittedly, we could have determined the angle of attack with the lowest drag coefficient and then rearranged the equations accordingly to solve for the cruise, but we decided to just find the lift and drag coefficients at 50 knots to start. By plugging our cruise parameters into the lift coefficient equation, we found that we would need a lift coefficient of 0.3627 to maintain level flight at cruise. We also recalculated our Reynolds number using our cruise parameters and we found that at a Reynolds number of 5.00 E^4 and a Ncrit value of 9, we would need an angle of attack from -0.25° to 0° to achieve the required lift coefficient. Conveniently, the drag coefficient is at its lowest between an AOA of -0.25° to 0°! We were super lucky in guessing a cruise speed that happened to align with the lowest drag coefficient and we would have otherwise had to rearrange the equations and take a slightly different process to determine the optimal cruise velocity. These calculations told us 2 important things:
- When the spars of the wing are horizontal, the wing is actually at a 2-degree angle of attack. This is necessary to simplify some dimensions in the design and it means we’ll have to mount it at a negative 2-degree angle at the fuselage so that it has a net AOA of zero degrees.
- At cruise, the wing will have an AOA of zero degrees.
Once we finished our calculations, it was time to implement them into our wing design. Over the past couple of months, we’d been collecting a list of small changes we’d like to implement into the wing so we did a little more than just increasing the reference area. Here’s a change list:
We updated the false rib design (curved orange part) to be simpler and stronger. The previous false rib design was inspired by those used in the popular BeLite ultralights. However, the BeLite ultralights use carbon fiber and aluminum while we use house insulation. The new ribs are simpler in form and should be easier to manufacture using a hot wire.
We revised the drag strut holes in the wing to be pill-shaped instead of ovals. We realized that it would be very difficult to make a precise elliptical hole, and the pill shape forms a cleaner hole in the rib to allow the passage of the drag struts.
The tops and bottoms of all ribs are now covered by a thin 3/32” strip of aircraft grade birch plywood. While we haven’t yet constructed any ribs or done any testing of our own, ultralight enthusiast Ian Lea’s rib tests suggest that plywood strips can significantly improve the strength of ribs for only a little additional weight. These strips will be epoxied in place during construction.