In the early 1980s a tethered balloon was ripped from its upwind tie-off ropes by a microburst. The insurance company which had coverage on the balloon commissioned an engineering study of the accident to help determine what happened. The following information has been edited to shield the parties involved and still demonstrate the forces that wind can have on a balloon. Editor
This study was generated as a result of an incident in which an AX-7 hot air balloon was struck by an unexpected wind squall on an otherwise calm and peaceful day. The balloon was accelerated by the wind until its two tether ropes tightened to arrest its motion; they broke just after the balloon’s envelope was ripped open, possibly by a tree, or else by the hoop tension stresses in its fabric, developed by the gust. Since this is not a routine engineering event, some research was needed to determine what loads acted upon the balloon, and the results of this investigation are the subject of this report. Some of the research—the determination of the virtual mass of a collapsing balloon canopy, for example—was at the time believed to be new. The rest of the findings are the application of normal analytical engineering techniques to a totally new problem
The Accident
A balloon had been conducting a tether operation in calm conditions for several hours. The location was a parking lot and the balloon had two upwind tether lines. One line was connected to a sport utility vehicle and the other to a light truck. A third tether line was used as a ground control line and controlled by a crew member.
What happened at the scene was recorded by photographs from three still cameras and one movie camera. The movie camera recorded approximately the last half to two- thirds of the accident.
Based on the photographic evidence it was determined that during normal operation the balloon was 23 feet off the ground when the tether lines were taut. The line to sport utility vehicle was 46 feet long when unstretched, and the line to the light truck was 38 feet long. With the balloon stationary and the tethers taut, it was 40 from the sport utility vehicle and 30 feet from the light truck. The length of the control line was not established and not important to the incident.
At the time of the incident the balloon basket was sitting on a wall. A gust of wind hit the envelope generating false lift lifting the basket off the wall and starting to further tighten the tether line to the sport utility vehicle. At this point in time the line to the light truck did not have any tension in it.
The line to the sport utility vehicle failed. Witnesses reported hearing the noise of the line breaking. The failure occurred about six feet away from the sport utility vehicle so that there was no question of a stress riser in a knot in the rope causing the failure. Testimony also noted that the sport utility vehicle moved backwards in a series of short sharp jerks prior to the line failing.
The basket returned to earth and fell on it side. The line from the light truck at this point is taut. The balloon envelope is about half deflated and a rip has developed along one side. At the time of the accident it was generally assumed that the rip was caused by contact with a tree.
Further investigation and analysis suggests that it is possible that the rip occurred earlier and was entirely due to wind pressure differential on the envelope. When a balloon is hit by a sudden gust, the windward face is compressed, raising the pressure of the gas inside. The air flow around the outsides of the balloon causes a reduction in pressure below ambient. So with a combination of higher than ambient pressure inside and lower than ambient pressure on the outside, the differential is sufficient to induce a hoop tension which can generate failure of the envelope material.
The next wind gust accelerated the balloon at an estimated .5 g to a speed of just under twelve feet per second. The remaining line to the light truck became taut and the speed of the balloon slowed. At this point the light truck was being pulled across the parking lot until it came in contact with a curb. At that point the light truck stopped moving and a tensile shockwave is believed to have started running along the rope and then reflected back causing failure of the rope. Whether or not that is true, the aerodynamic drag on the balloon was now of the order of 12,500 pounds which is well in excess of the rated strength of the rope. The basket, which still contained the pilot, then accelerated at approximately 1.5 g.
The acceleration of the basket was stopped, momentarily, when it struck a glancing blow on a small car parked on the street.
At the point in time when the line to the light truck broke the third control line was still being held by several crew members. Within milliseconds the line became uncontrollable and ran through their hands giving many of them rope burns. At that point they were trying to oppose a force of 5,000 pounds. One person’s leg began tangled with the control line and they were dragged, first hitting a wall, being “slingshot” over the wall, and then coming in contact with the same small car that the basket had. The individual hit the car with a glancing blow and rose approximately six feet in the air. It is believed that the impact against the car caused tensile shock waves up the line and their reflection is probably what unwound or at least assisted in the unwinding of the line from the individuals leg, allowing them to fall onto the hood of the small car. All of this has taken place in about ten seconds. The balloon continued flight and its estimated speed as it goes over a house across the street is approximately 19 feet per second, or about 13 mph and accelerating.
Analysis
First thing that must recognized is that a dainty, flimsy, hot air balloon, so light that it floats in the insubstantial air, is something of an illusion. It really weighs about three tons, and when moving, has an inertia equivalent to about five tons. That is the mass of 67 people. It also has an enormous drag area, larger than the largest sail ever hoisted on a sailing ship. So if a gust of wind hits a balloon and gets it moving, this enormous behemoth is going to take a lot of stopping. And the stopping has to be done very carefully.
The weight of a balloon is equal to the weight of the air which it displaces. This is the principle discovered by Archimedes about 300 years before Christ. It is also the reason that ships float on water; the weight of the water they displace is equal to their weight. In air, at sea level, a 55 feet diameter sphere displaces more than 77,000 cubic feet and since air weighs about .076 pounds per cubic foot, the total weight is about 6,612 pounds. We cannot “weigh” this weight on a pair of scales because it is supported by the buoyancy of the atmosphere. But it clearly represents inertia when moving, just as a weightless ship out of control does a great deal of damage if it runs into a lock gate or a dock.
Actually a balloon is even more massive than appears from this simple reasoning because when it moves through the atmosphere or a wind blows so that the atmosphere moves with respect to the balloon, the air outside the canopy is also influenced by it presence and this acts as additional equivalent mass so that when the balloon is moving it contributes additional momentum or inertia. The reader can study this effect for himself by filing a sink full of water and then ringing a tuning fork, first in air and then underwater. Because of the “added mass” of the water (which is about 800 times heavier than air) the frequency of the tuning fork is lower underwater than it is in the air. If the tuning fork were rung in the vacuum of space, it would oscillate at a higher frequency than in air, but of course one wouldn’t be able to hear it because sound waves don’t transmit through a vacuum. This “virtual mass” effect associated with a spherical shape is demonstrated by how it slows the ascent of air bubbles in a water cooler, an effect familiar to most office inhabitants.
The “virtual mass” in the air outside a body such as a balloon depends on the details of the shape. Much less air is affected by a spherical shape than, say, one which is cup shaped. So if a balloon is collapsing the virtual mass is increasing. This change is virtual mass leads to increased pressure forces acting on the balloon and one of the original contributions of this report is to determine just how much this change is. Secondly, even if the balloon shape were not changing, the virtual mass of the air outside it leads to additional forces when the wind speed increases with time rather than remaining constant, and these forces can be much greater than the simple steady state aerodynamic forces that we are mostly familiar with.
The “steady state” drag forces acting on the balloon are also a function of its shape so that these are also changing if the balloon is collapsing. These are the forces that we think about as acting upon a sail to drive a boat along and unlike the “virtual mass” induced forces they are independent of the rate at which the balloon collapses depending only on its shape at any instant that they are computed.
The rate at which the balloon collapses and therefore the magnitude of the transient aerodynamic forces depends of course upon the magnitude of the wind, the rate at which the wind is increasing (hence giving rise to transient virtual mass forces) and the size of the hole through which the hot air inside the balloon is able to escape. It seems that in the present accident, a hole was opened in the [envelope] by the balloon hitting a tree. However, it is also possible that that hole occurred before tree impact because the stresses generated in the envelope by the external aerodynamic pressures must have been quite close to those necessary to cause failure of the material without the need for contact with some sharp object. (Cases have occurred where a balloon envelope has ripped in free flight well away from the ground due to a sudden change in wind velocity.) In the present case it’s possible to roughly calculate the area of the hole in the side of the balloon from the photographic evidence. The opening of the mouth of the balloon is know from the manufacturer.
The last effect to be discussed is that of slack in the line. Suppose that the breaking strength of a line is 4,000 pounds and that the aerodynamic drag of a stationary balloon in a 30 mile-per-hour wind is only 3,000 pounds. Then further assuming that this tether line is parallel to the wind direction (which is almost never is, of course, so that the loads are then higher), one would expect it to hold. But if there is 30 or 40 feet of slack rope, the balloon will accelerate to some speed, say 10 mph, before the rope tightens. Now, remembering that the balloons has a mass equivalent of 10,000 pounds, it’s easy to see that the forces developed to arrest the motion of this very large mass, can be much greater than the 4,000 pounds breaking strength of the rope. As a matter of fact, the magnitude of these decelerating forces depends primarily on the elasticity of the rope. The more give it has (the more stretchy) the lower will be the inertia forces due to arresting the balloon. So the injunction to “use a stronger rope” is fairly meaningless. If one used an identical type of rope but of twice the diameter, it would be four times as stiff, have one-quarter the deflection, and so the inertial forces developed would be four times as great and it would still break. This is an oversimplification because there are steady state aerodynamic forces involved in the total rope force and they do not vary with the “give” of the line.
It was determined that the operation of the balloon was in conformity with general good practice and there was little chance that any conceivable precaution could have prevented the accident which occurred. Using much stronger ropes might have transferred the failure mode to the attachment point on the basket. On the other hand with ropes that heavy, it’s problematical whether the balloon could even have risen carrying passengers, thus defeating the whole object of the exercise. It is suggested that the operator would have been safer, in hindsight, to have foregone the use of a control rope with the ground crew, and instead controlled the rise and fall with the two ropes attached to the vehicles so that there was never any slack in the system. But this would be a much more ponderous operation and would require special snubbing provisions at one or both attachment points. Alternatively if the operator could have used somewhat lighter automobiles standing on a large unobstructed area, so that they could be dragged when the loads exceeded the friction of their wheels on the tarmac, this would have taken the energy out of the system in a load-limiting way and would have reduced the strain in the ropes. Some of this actually happened in the present accident but then the vehicle struck the curb and was prevented from traveling any further; after which it was “all over” for the rope attached to that vehicle.
Another way of preventing attachment line failure would be to use energy absorbing devices at the attachment points. The ideal device, which may not be available, would be a double capstan, around which the line was passed a number of times, one or both of the capstans being attached to a rotary brake with a maximum setting less than the breaking strength of the rope. The brake would normally be off and the ascent and descent of the balloon would be effected by pulling in or letting out on the rope. In one version of this, one attach rope could be attached to some appropriate anchor and be always taut whether the balloon was on the ground or at its maximum height. In this case the balloon would be describing an arc about the attachment point, its height controlled by the second capstan brake mounted line. Then if trouble developed the brake could be engaged on the capstan line, or could even be arranged so that the brake kicked on when the rotational rate of the capstan exceeded some critical figure.
Final Thoughts
The microburst which caused this accident came from thunderstorm activity more than 50 miles away. Although the operation was being conducted in an acceptable manner, the incident reinforces the point that when conducting a tether operation it is important to be prepared for the unexpected. That includes the use of proper equipment, procedures, and gathering weather information for the region, not just a specific location.
Wind is a fluid and can exert tremendous force. A balloon has an enormous drag area. When wind comes in contact with an object, such as a balloon, the resulting force is going to be very difficult to stop—and it must be done carefully.