Wing-loading and Parachute Performance
It is common knowledge that wing-loading has profound effects on the way parachutes perform. Furthermore, it appears that even if the wing-loading is exactly the same between two otherwise identical parachutes, different size canopies fly quite differently. In other words, if you fly a 210 square foot parachute of a given design with lots of additional weight to achieve a loading of say, one pound per square foot, a 150 at the exact same wing-loading will usually have a steeper glide ratio, faster turns, and demonstrate a longer recovery arc following a high airspeed maneuver. This means that, regardless of the wing-loading, all small canopies are high performance, and should be treated accordingly. There are many explanations for this non-linear relationship, and in this article I will discuss some of the most significant governing variables.
Test flight data shows us that small wings, regardless of wing-loading, will be more radical than their larger counterparts, all other design aspects being equal, however the degree to which they are different depends of the model of the canopy. Nevertheless, the trend is consistent and predictable. The most common explanation for these differences is that it is due to differences in line length. Smaller canopies do have shorter lines on the whole. Although it is true that some aspects of a parachute’s performance increases as line length reduces, this only applies to mobility about the roll, pitch and yaw axis. The effects on recovery arc tend to have the opposite response to line length. In other words, a parachute with longer lines tends to exhibit a longer recovery arc. To explain these counter-intuitive effects, we must look elsewhere for an explanation.
The other aspect, previously unconsidered, is the relationship of the canopy's internal volume to its surface area. Essentially, the volume displaced by the airfoil can be thought of as a key aspect of the overall DRAG. Of course the shape of the wing itself is vitally relevant to the drag coefficient, but for the purposes of this discussion, let’s focus on the effects of drag from the perspective of simple air displacement, like a footprint in the sky. The fatter the airfoil, the more drag it will exhibit. This means that a “fat” parachute will sit at a higher angle of attack in full flight, based on the balance of power between the airfoil's drag (D1) and that of the suspended load, the jumper (D2). Further, the drag value of a “fat” airfoil will increase markedly with airspeed, and therefore large objects will suffer more drag than “skinny” airfoils at high speed. The wing, therefore, will “want” to return to the overhead position more aggressively on fatter airfoils, as a general rule.
Let's take those aerodynamic principles to the realm of parachute sizing. When a parachute design is scaled, for the most part, the entire wing is scaled simultaneously. This is the same geometric progression as a matchbox car: same three dimensional proportions, but a different size. When we want to make a parachute larger, we simply multiply each dimension by a “scale factor”, a single number that will result in the size change we desire.
When we apply this mathematical model to parachute designs, we create an unwanted effect: disproportionate scale factors relating to area and volume. Simply put, the number we use to scale the parachute is based on the "square footage" of the wing, and this is of course, a square function (X²). The volume on the other hand, is governed by a cube function, (X³). This means that when we increase the height of the rib at the same rate as the span and the chord, we inadvertently make the wing too fat as we scale upwards, and too thin when we scale down. This is one of the reasons why a 120 flies very differently than a 170, even at the exact same wing-loading and body drag component. The wings only appear to be the same, but they are most decidedly not the same from a volumetric perspective.
So, one might say, why don't we make the height of the airfoil on smaller wings greater, and that of larger wings smaller, proportionately? This is sometimes done and it works to a certain degree. However, if we were to search for a formula that would allow us to scale the volume at the same rate as the area, we would have to keep the rib height the same on all sizes of a design. I worked this out with a brilliant Tasmanian mathematician on flight back from Sydney many years ago. A 120 with the same rib as a 190? That doesn't quite pass the gut check, does it? Only the middle sizes would fly right, and beyond a few degrees of freedom, the system would collapse into chaos, because the fat little wings would have too much drag to be efficient and the big wings would have too little lift to land well, and would be prone to collapse in turbulence due to their flimsy nature by virtue of their low volume. A simple answer does not appear to exist, at least not yet.
The heart of the problem is the fact that our industry has grown accustomed to the use of "pounds per square foot" as our way of quantifying parachute size. This leads to the erroneous belief that a given "wing-loading" will result in similar performance for all parachutes regardless of size. This is most certainly not the case, and is dangerously misleading for light weight jumpers striving for that magical one pound per square foot wing-loading. A 120 is inappropriate for someone with less than 100 jumps no matter how much they weigh. So, what do we do? Firstly, we honor the differences in parachute sizes, and downsize very carefully. We make our steps downward based on actual ability and frequency of jumping, and we look for any excuse we can to upsize. In addition to remaining conservative with regards to canopy size, we must go to greater lengths to understand the nature of performance and size.
If it is true that performance trends do not appear linear with regards to parachute size, then perhaps the solution is a curved ruler. To that end, I have offered a complex sizing chart to the world that reflects the non-linear nature of parachute sizing and performance for the purpose of downsizing guidance. This easy-to-operate chart has been adopted by many national organizations and local dropzones as the official guidelines for parachute size relative to experience. Born from a brilliant but arguably conservative Swedish chart created by my good friend and colleague, Ola Jameson, who was the Head of Safety (Riksinstructor) for the SFF at the time. My somewhat less conservative version of the “sizing chart” offers suggestions for parachute size relative to weight, rather than simple wing-loading alone as the defining factor. This allows the recommended parachute size for a heavy person to be a higher wing-loading than that which is suggested for a lighter person. It is available HERE.
The sizing chart does not suggest when the jumper should downsize, but rather limits the degree to which they should decrease their parachute size based on the complex aerodynamic principles effected by wing geometry. The "chart trap" is always a risk with such things, when jumpers automatically step down in size because the chart suggests that a change is reasonable. Decisions based on parachute size and design should always be made based on the actual ability of the jumper, and the other governing factors described in the 22 pages of modifying text that follow the chart.
Another consideration I will now put forth to the skydiving community is a fundamental change to the way we define parachute size. Based on the discussion above, a two-dimensional analysis is insufficient to describe what a parachute will do in the sky, and "pounds per square foot" is a very limited 2-D relationship. I suggest that a better model for parachute size definition is Pounds (or kilos) per Cubic foot (or cubic meter). The metric numbers would be far easier to work, if we can get the Yanks and Brits to let go of the Imperial system; but we have to pick our battles, don't we. By using lbs/ft³, we will effectively remove the 2-D bias from the "ruler" as it were, and make the relevant differences more numerically obvious. It may sound like a radical idea at first, but so was the ram air canopy when that showed up, but look how well that worked out. Just because a change is difficult does not make it less necessary.
In the interest of moving this new paradigm forward, and in the spirit of the immortal words of Mahatma Gandhi, I will be the change I wish to see in the world. Here are the volumes of my parachutes. It is my hope that other manufacturers will follow suit, in the interest of transparency of our parachutes’ designs, for the good of the skydiving public.
The topic of parachute performance prediction is vast, and must continue to be discussed in scientific terms. We must do this because, as one of the few (mostly) self-governing branches of aviation, we are the only true experts in our field. We are the ones who must think outside the old box of established paradigms, and change when change is necessary. We will continue to improve our sport in every way, simply because we love our sport so much that we want to know more, and grow more. The universal passion for knowledge exhibited throughout the skydiving community leads us to a very high level of mutual respect for our fellow jumpers. This precious commodity of solidarity is rare in this world, and we must allow that connection to lead us to always reach for safer procedures built on our ever-increasing understanding of that which saves our lives. Improvement in matters relating to safety is just love of life in motion, and love must be adaptable and smart if it is to last in a complex world. Again and again, skydivers prove to me that they are highly intelligent adventurers committed to safety, and very much worthy of my respect. We will adapt, and we will thrive.
About the Author: Brian Germain is a parachute designer, author, teacher, radio personality, keynote speaker with over 15,000 jumps, and has been an active skydiver for 30 years. He is the creator of the famed instructional video "No Sweat: Parachute Packing Made Easy", as well as the critically acclaimed book The Parachute and its Pilot. You can get more of Brian’s teaching at Adventure Wisdom, Big Air Sportz, Transcending Fear, and on his vast YouTube Channel
Ever since I was a student, I've always wondered about the scaling of canopies, and whether or not they followed the concept of similitude, but generally assumed they didn't.
Wouldn't it make sense to design a canopy around an ideal size / WL / performance, and then scale according to the fluid dynamics to achieve the "standard sizes", in attempts to try and create a more consistent relationship to the flight characteristics?
This is a great idea when you look at it from the perspective of 'rule making' - even if you want to celebrate your optimal freedom and only live by 'rules of thumb/dumb'. However, like the famous 'do not take a camera with you unless you have xx jumps' I could also see something happening like 'do not exceed a ratio of 0,xx' in the volume of your parachute divided by its area unless you have xx jumps'. It is clear that this ratio which ranges from 0,42 for Big Air Sports smallest canopy to 0,65 for its biggest one could give you (and those trying to prevent you from hurting yourself by making dents in their dropzones) an extra handle when assesing your ability to handle a certain canopy.
To clarify the method I used for calculating internal volume:
Span x Chord x [*Rib height]
Rib height = maximum rib height divide by two, averaged value of all ribs
This is not an exact figure, however it is an expedient way to make the calculations. If the math takes too long, other manufacturers are not likely to measure their volumes. If all the manufacturers use this method, we will level to playing field and make volume comparisons across products a quite valuable number.
That said, the total number of ribs alters the inflated volume of the canopy, a fact which must be taken into account. In other words, a standard seven cell will have a larger inflated volume than a nine cell with the exact same ribs. I am not yet clear on how we will factor this into the equation, but acknowledge the necessary of this amendment.
Again, the goal of the use of this number is to help parachute customers to have another metric to predict a parachutes performance beyond just 2-D area. There is no doubt that other variables have a huge impact on parachute performance beyond area and volume alone. These variable include: (elliptical taper, line trim, line length, location and duration of max rib height, line attachment displacement, fabric type, line type and diameter, number of stitch rows and thread type, and undoubtably several others that I have not thought of in this moment. Nevertheless, volume is a significant feature, and the customers should be able to compare differences between designs.
I have been thinking about the effects of volume on size more since I wrote this article. I believe that that balance of power between D1 and D2 as it relates to scale has a profound effect on the flight characteristics. Given the fact that canopy drag changes while body drag does not, large canopies; even with an adjusted airfoil height, will never have as long a recovery arc as their smaller counterparts. Likewise, large canopies will always have a higher pitch angle in full flight due to their higher drag value, and will consequently have a flatter glide ratio. That said; the non-linear scale effects are still something to be considered, as are the differences between canopy designs. We need to consider all of the variables if we are to accurately predict a parachutes flight characteristics, and any single metric will be insufficient.
More articles in this category:
- 4 Smart Questions That Shut Down The Spin Cycle - by Annette O'Neil (Posted: 2016-01-14)
- Wing-loading and Parachute Performance - by Brian Germain (Posted: 2015-10-19)
- Stalling For Success - by Annette O'Neil (Posted: 2015-08-06)
- It's Not Only Size That Matters - Thoughts on Canopy Upsizing - by Dave Kottwitz (Dusty Dave) (Posted: 2014-05-09)
- When Should You Upsize Your Canopy - by Melissa Lowe, Barry Williams and Jason Moledzki (Posted: 2014-02-25)
- Saved By The Beep - by Brian Germain (Posted: 2011-05-15)
- The Abort Zone - by Brian Germain (Posted: 2010-09-01)
- An Inconvenient Truth Regarding PLF's - by Jack Guthrie (Posted: 2010-03-02)