Rocketry Planet

The Tripoli Wisconsin Association's (TWA) launches have drawn more and more fliers from farther and farther away. This has been good and bad. The 'bad' can include long waits between flights due to the number of people flying. The question of how to solve the problem was asked.

A mathematical model of range operations was developed, which lead to suggestions for changes that could increase the number of flights that can be made per day. Anyone who has received a sunburn while waiting for a launch pad assignment and then waiting for the rocket to leave the Earth should immediately comprehend the math.

It's not complex, and it can be fun.

When this analysis was written TWA had 12 launch pads for high power rockets. The pads usually have a launch rod mix of five or six 1/4" rods, one or two 3/8" rods, 1/2" rods and a couple of rails. The demand for rod sizes differs from day-to-day and hour-to-hour. Sometimes the most demand is for 1/4" rods, and sometimes for 1/2" rods.

Due to space and safety issues the launch pads are physically grouped together. All pads are loaded at a time and then the rockets are launched. Although the area where TWA flies is large, the space where the launch pads can be placed is small.

TWA flies in a state park that was an Air Force base. The pads are positioned on compacted gravel that used to be a runway. The surrounding area is prairie grass. Sufficient space is not available on the old runway to position the pads so that they can be loaded and launched concurrently. Pads cannot be placed in the prairie grass due to the risk of fire. Although the runway is 2.5 miles long it isn't wide enough to load and launch concurrently while meeting the minimum safe distance requirements.

The factors used in the equation need to be defined. They are listed below:

t =	Maximum flying time. 10 hours = 600 minutes.
d =	Down time due to shift changes, announcements, etc., per day. Assume 30 minutes.
r =	Sets of rockets that can be flown per day.
l =	Launch pad load time. This is the time to walk to the pads, load a rocket, install and attach clips to the igniter, aim the rocket, and walk away from the pad area. Assume 10 minutes per set no matter how many pads are in the set.
p =	Pads per set.
f =	Average flight time per rocket. This is the time to announce a flight, launch the rocket, and wait for recovery system to deploy before the next rocket can be launched. Assume 2 minutes. The average should include downtime caused by aircraft in the launch area, clouds, and other unpredictable events that cause delays.

The best case is one launch pad per flight to reduce the launch pad loading time to the smallest value, which is impossible for many reasons, including that all rockets are not ready to fly at the same time, but it provides a starting point. In this case the equation becomes

total flight time = 600 - 30 - 10 = 560 minutes and the maximum number of flights per day is minutes / 2 minutes per flight = 280

The most significant factor in this case is the flight time. A reduction in flight time increases the number of rockets that can be flown per day. This case is unrealistic as all rockets are not ready for flight at the same time, and 300 launch pads are not available.

Due to space limitations, TWA must group the launch pads together and load them as a set. The number of rockets that can be flown per day, assuming a fixed, average launch pad loading time of 10 minutes, depends upon the number of launch pads in the set.

r = (t - d)/(l + (f * p)) r = 570/(10 + (2 * p))

Pads per Set=01 Sets=50 Max. Flights=050

Pads per Set=02 Sets=42 Max. Flights=084

Pads per Set=03 Sets=37 Max. Flights=111

Pads per Set=04 Sets=33 Max. Flights=132

Pads per Set=05 Sets=30 Max. Flights=150

Pads per Set=06 Sets=27 Max. Flights=162

Pads per Set=07 Sets=25 Max. Flights=175

Pads per Set=08 Sets=23 Max. Flights=184

Pads per Set=09 Sets=21 Max. Flights=189

Pads per Set=10 Sets=20 Max. Flights=200

Pads per Set=11 Sets=18 Max. Flights=198

Pads per Set=12 Sets=17 Max. Flights=204

Pads per Set=13 Sets=16 Max. Flights=208

Pads per Set=14 Sets=15 Max. Flights=210

Pads per Set=15 Sets=15 Max. Flights=225

Pads per Set=16 Sets=14 Max. Flights=224

Pads per Set=17 Sets=13 Max. Flights=221

Pads per Set=18 Sets=13 Max. Flights=234

Pads per Set=19 Sets=12 Max. Flights=228

Pads per Set=20 Sets=12 Max. Flights=240

With the assumptions given above, the maximum number of high power flights per day that the 12 launch pads used by TWA can support is about 200.

Modifying the assumptions can produce significant changes in the maximum number of flights per day. For example, if the average flight time is only 1 minute and pad loading time is 5 minutes then the maximum number of flights doubles. If pad loading time is driven to zero then the maximum number of flights leaps to 600!

Adding more pads reduces time lost to loading the set of pads over a day. However, the increase in number of flights with more pads is not significant. Doubling the number of launch pads from 12 to 24 only produces an increase of about 40 flights at a great cost. The cost of additional equipment and the time cost to setup more pads may offset an increase in the number of flights.

Launch pad loading time can be driven to zero by using multple sets of pads so that one set is launched while the other is loaded. As long as launching and loading occur simultaneously no time will be lost. This isn't always possible, of course as clubs may not have enough equipment or space for multiple sets of launch pads.

To reduce the pad loading time to zero, two sets of pads would be needed so that the time to load one set is offset by the flying time for the other set. Each set of pads should have about 5 pads.

Pads per Set = 10 minutes loading time / 2 minutes flight time = 5

This result is only valid if all launch pads use the same rod size and everyone needs one rod size. That's not true, of course. But it would be if rails were used rather than rods.

If the average flight time is 1 minute then the number of launch pads per set should be increased for the optimum number of 10 for non-stop flying.

If two sets of launch pads cannot be used and the average flight time cannot be reduced, then the only factor that can be affected is the launch pad loading time. That factor can be reduced by using rails rather than rods and having staff at the pads to assist rocketeers.

Rails help reduce launch pad loading time because "one size fits all". When rods are used time can be lost due to the need to swap rod sizes. If rods cannot be changed then some launch pads may stand empty due to a mismatched supply and demand for rod sizes. If 6 of the 12 launch pads have 1/4" rods but most people want 1/2" rods during a 1/2 hour time period then the launch pads will not be efficiently utilized. A costly solution is to have multiple sets of launch pads where each set has a different launch rod size to ensure that a sufficient number launch pads with each rod size is available.

This analysis assumes a uniform number of flights over a day. That is usually not the case. Most flights at a TWA launch occur after noon. No pad arrangement will solve that situation. This is partly caused by the need to wait for the motor vendor to arrive for motor delivery, and then the time needed to assemble a motor and perform other flight preparation work.

One way to solve the problem of having enough launch pads and the right mix of launch rods is to have more pads than needed so that there will always be a sufficient number of rods of each size (1/4", 3/8", 1/2", etc.). However, that's a costly solution, but one that is utilized by some clubs and large launches. The maximum number of flights is still dependent on the average flight time.

The best situation is a set of launch pads with rails that can be loaded and launched concurrently, if enough space is available for placing launch pads 200-300 feet apart, and to have distant pads for large motors and rockets that take a lot of time to prepare. The optimum number of launch pads depends upon the average flight time (l / f + 1). If we assume that the average launch pad loading time is about 10 minutes and the average flight time is 2 minutes, then six launch pads (10 / 2 + 1 = 6) should allow continuous launching, and nearly 300 flights per day. With launch pad loading time effectively zero, the shorter the average flight time the greater the number of rockets that can be flown per day.