Content copyright . Brad Evans. All rights reserved.
AGM-78 Standard Missile (Raytheon) 3/5 Scale
I) Introduction
A) General narrative description of model including:
1) Describe dimensions (length, diameter) and launch weight
The full scale AGM-78 “Standard Missile” built by Raytheon is 13.5 inches in diameter with a length of 15 feet. Original 1977 plans were obtained in order to establish proper dimensions. The plans provide stations giving some exact dimensions including width and fin/strake spans. Since exact fin/strake lengths were not in the plans, they were built using calipers in proportion to length. This 3/5 scale AGM-78 scaled based on available airframe materials (nominal 8” diameter) and the exact diameter was used to establish scale. The complete design was created using RockSim software (Apogee) and the entire build from scratch was posted on a dedicated website page on (http://therocketdoc.com). The final dimensions are 8.25 inches in diameter and 9.4 feet in length, and the pad ready weight is 45 pounds.
2) Planned motor
The motor will be an M1297 W
with a 98mm Aero Pack retainer with a 75mm adapter.
B) Narrative description of flight operation including:
1) Expected altitude:
According to the RockSim simulations, at a pad ready weight of 45 pounds, the expected altitude is ~4200’.
2) Recovery system operation:
This is a dual deploy recovery.
C) Any novel or unique design features:
The most unique aspect of this rocket is the presence of both aft fins and strakes that combined run approximately 2/3 the length. The strakes run across the airframe break over the altimeter bay that is built into the upper airframe. While the fins were easily placed in the rocket in a standard manner, the addition of strakes presented a unique challenge.
D) Any major risks and mitigation of those concerns:
1) There are two major risks for this flight. The first is unstable flight of a unique design. This has been addressed by building a 4” diameter prototype of this rocket using identical concepts. The build is documented under the Projects tab of the http://therocketdoc.com website. The prototype was flow successfully on two occasions using motor deploy. The predicted altitude for these flights was ~5,000’. The timing of the successful deploys was consistent with this prediction. There were no altimeters on-board.
2) The other risk is deployment
failure. This is mitigated by the use of redundant altimeters and deployment
charges.
II) Scale drawing showing:
See the RockSim simulations
A) May be a hand drawn or computer graphic
B) Major dimensions (dimensions used in CP calculations should be shown)
C) Calculated center of pressure
D) Aft CG limit
III) Description of construction materials and techniques (Construction Package)
A) The unique aspect of the rocket
is the presence of strakes and fins that combined run 2/3 the length of the
rocket. This required new construction techniques. The aft portion of the
strakes needed to be solidly epoxied to the centering rings and the motor tube
using three fin tabs. Because of the length of the fins and the length of the
strakes in the lower airframe, a 32” length of 98mm motor tube had to be used
for the through-the-wall construction. The forward end of the lower airframe
was doubled down to the forward centering ring. This allowed for a ~1/8” cut to
create a track for the strake over that area. The altimeter bay is not
permanent. The upper and lower bulkheads could be removed to add charges and a
hatch allowed access to the altimeters and switches. Since the altimeter bay
was placed at the aft end of the upper airframe (that was also doubled full
length), a ~1/2” deep track was created over the bay and a ~¼” track was made
forward of the bay to the end of the strake. The strake broke at the end of the
upper airframe and each had to be lined up perfectly with each segment and with
the fins for stable flight. The nose cone is custom built in proportion to the
original 1977 Raytheon plans. A screenshot was made of the plans, and the
nosecone portion was blown up to an 8.25” diameter creating a 16” long cone.
The cone is built from an 8” long doubled coupler with 1 inch Styrofoam blocks
around an approximately 54mm central cardboard tube. The central tube also
provides a cavity in which lead shot can be introduced for weight and balance.
A 3/8 all thread is placed in the central tube and anchored to the base of the nose
cone tip with several ounces of epoxy. Sequential ½” birch ply centering rings
between 2” of Styrofoam provide shape for the cone consistent with the two
dimensional plan. They also provide a guide for sanding to maintain the cone
shape. Carefully removing excess foam produces the planned shape that becomes
the glassing form. The tip of the nosecone was made using West Systems epoxy
with light weight fairing filler. The mixture was poured into a polyethylene
filter slightly larger than the planned cone tip size. After curing, it was
band sanded to the proper dimensions. The 3/8” all thread runs the length
of the cone. The central tube continues flush through an aft centering ring
recessed ½”. This allows for the aft bulkplate to fit over the bulkhead covering
the central tube and sit flush to the base of the coupler. The all thread runs
through this bulkplate ending with a 5/16” galvanized eye-bolt that tightens to
the aft bulkplate. This bulkplate is also bolted into the aft bulkhead with
four 5/16” bolts. In this way, the bulkplate can be easily removed so that lead
in the central tube can be removed or added at the field for final weight and
balance. After the fins and strakes were first attached to the centering rings
and motor tube and aligned with the fins, a unique challenge presented itself
to fully epoxy all internal contact points and then to rigidly finish the fin
canister with internal urethane foaming. Closed compartments were created when
the strake tabs were placed between the centering rings. To address this
problem, each of the centering rings forward of the aft bulkhead had four ¾”
holes drilled symmetrically ending up between each fin tab. Using a funnel and
½” polyethylene tubing was used to add approximately 3 ounces of West Systems
105/206/404 filler to each of the compartments from forward to aft with the
airframe held horizontally in its cradle. The airframe was rolled manually a
quarter turn every 10 minutes for 3 hours. Urethane foam was added to each
compartment from forward to aft in the same manner after the epoxy was cured
for 24 hours with the lower airframe turned upright until the entire canister
was filled.
B) Airframe materials including
1) Airframes were made from readily available 8” nominal concrete construction Sonotubes. The waxy liner had to be peeled away as was the outer paper covering.
2) Fins and strakes are made of 3/8” composite sheet distributed by Giant Leap Rocketry. It consists of a layer of Nomex coated with a thin layer of fiberglass sheet.
3) Centering rings, bulkheads and bulkplates were all made were all made of ½” three-ply birch.
4) The launch pad was custom built and is shown on the http://therocketdoc.com site. The launch rail is 1515 8020, Inc rail. Launch lugs are Delran buttons.
5) Reinforcement materials: The airframes were polyester socked (Giant Leap) and painted with one coat of West Systems 105/206 slow cure epoxy resin. The airframes were rotisserie rolled until cured. After the fins and strakes were attached, Giant Leap two-part heat resistant urethane foam filled the entire fin canister to solidly hold the fins and strake tabs to all internal surfaces.
6) Adhesives: Two-part 30 minute cure hobby epoxy was used primarily. The fins and strakes were initially attached to the centering rings, motor tube and airframes with West Systems 105/206 fast cure epoxy resin mixed with 404 high strength adhesive filler. All internal fin/strake contact points were epoxied using West Systems 105/206 slow cure epoxy resin with 404 high strength filler. All fillets were made of West Systems 105/206 epoxy resin mixed with 407 light fairing filler.
7) Nosecone was fabricated using alternating rings of Styrofoam and ½” 3-ply birch centering rings around a central cardboard tube. The cone tip was created from molded West Systems epoxy resin. A 3/8” all thread connected the nose tip to the aft bulkhead.
C) Construction techniques including
1) Fin mounting method was through-the-wall
2) Reinforcement areas were located primarily in the fin canister at all internal contact points and surfaces.
3) There were no frangible or breakaway components
D) Drawing showing interior layout of components/airframe assembly
RockSim screen shots of flat plane and 3D views
E) Photographs
All are posted on http://therocketdoc.com
1) Show construction of areas hidden after assembly
2) Show details of construction
3) Include a size reference, e.g. coin or ruler
IV) Description of recovery system components and operation (Recovery Systems Package)
B) Description of operation
1) Describe deployment sequence
The drogue parachute will be deployed at apogee with 4gm FFFF black powder charges and the main parachute will deploy at 1300’ with 5gm FFFF black powder charges The secondary will have a drogue delay of 1 second and main will deploy at 1000’.
2) Describe mounting locations, riser connection scheme
3) Describe parachute compartments and closures
a) Drogue and main compartment sizes
a) 3 4-40 nylon shear pins will be used for the nose cone coupler to the airframe and 3 4-40 pins at the coupler of upper airframe through the lower.
b) Kevlar cloth (flight suit material) is used to protect both drogue and main parachutes.
4) Compartment venting:
Lower airframe is vented with two 1/3” holes based on formula:
The upper airframe has two offset 1/3” holes based on formula.
The altimeter bay has four offset 1/3” holes so that no vent is 180 degrees opposite another.
5) Descent rates for all parts
Calculations for descent rates were based on RockSim simulations
A main parachute was selected to produce a descent rate of 12’/second. This was selected because of the hard desert surface
The drogue chute was sized for a descent rate of 50’/second.
C) Description of components
1) Control devices
Two RRC2mini (Missile Works) altimeters will be used for dual deployment with barometric sensing
2) Parachutes
a) 36” drogue parachute
b) 122” main Spherachute with x” spill hole.
c) Parachute bags are not used
3) Risers
4) Mounting hardware
Two 25 foot, 1 inch tubular nylon harnesses will be used for both the upper and lower airframes. A short length of tubular nylon is attached to two 5/16” stainless steel U-bolts on the forward centering ring of the motor tube. A knot is made at the center of the short harness. The 25’ lower airframe harness is connected to that knot with a 5/16” Quick-link 5/16” and then to a 5/16” eye bolt on the all thread at the aft bulkhead of the altimeter bay. In this way, at least one attachment is maintained to a U-bolt should the other fail for any reason. The other 25’ harness attached to a 5/16” eye bolt at the forward bulkhead of the bay and then attached to a 5/16” eye bolt on the aft bulkplate of the nosecone. All deployment forces are distributed through the center of the rocket through the all thread that runs the length of the altimeter bay than through U- or eye bolts conventionally attached only to the bay bulkheads. 5/16” stainless steel Quick-links are used to attach the harnesses to their respective eye bolts.
a) Two charges are placed in PVC caps on each altimeter bay bulkheads. One is first from the primary altimeter and one each from the secondary
b) Perfectlite electric match are used and have been used successfully
c) Volume/weight of pyrotechnic materials 6.5gm drogue compartment and 8.0gm main compartment based on formula and ground testing
D) Recovery sequence initiation device testing and operation verification
1) Altimeters were testing under vacuum with live e-matches. 2) Prototype flown twice at Rainbow Valley, AZ (see http://therocketdoc.com for construction techniques and photos
3) Charges were ground tested
4) Recovery system initiation devices were previously tested on 6 previous flights.
VI) Stability evaluation
A) Launch pad custom built with 14’ width and 12 foot 1515 rail
B) See RockSim Printout for:
Center of pressure calculations:
Aft CG limit or actual CG
Actual CG
CG is a minimum of one body tube diameter ahead of the CP
Stability for complex shapes was verified by sub-scale model
Sub-scale model was 50% scale and CG locations should be scaled identically Flight tests should had approximately the same dynamics
VI) Expected performance/flight profile
A) Provide the following estimated flight parameters:
1) Launch weight: 44 pounds pad ready
2) Motor type
a) Aero tech M
b) Motor has a total impulse of 5120.01 Newton-seconds
c) Motor is currently certified by Tripoli
See RockSim for:
Estimated drag coefficient 4) Velocity as the rocket leaves the launch system
1) Maximum expected velocity
2) Maximum expected altitude
3) Maximum expected acceleration
4) Multiple profiles over a range of conditions are recommended when conditions are either estimated, unknown or variable are shown on RockSim
C) RockSim was used to determine the flight performance parameters
VII) Pre-launch checklist; typical checklist items include:
A) Equipment list including
1) Motor preparation materials, e.g. lubricants
2) Tools for airframe assembly and inspection
3) Electrical test items for voltage and resistance tests
4) Loose hardware (e.g. for motor retention, shear pins)
5) Safety equipment (e.g. face shield)
6) Comfort items (e.g. chair, table, and shade)
B) Safety practices
1) Identify items where pyrotechnics or hazardous items are being prepared, installed or tested
2) Identify precautions, e.g.
a) Safety equipment to be used
b) Safety procedures to follow
3) Require coordination of radio frequencies with other modelers to prevent interference
C) Motor preparation per manufacturer's instructions
1) Igniter installation is deferred until the model is on the launch pad
2) This item might be left until after the airframe is prepared in case of an
airframe problem
3) Install and secure the motor in the airframe
D) Electronics preparations
1) Verify safe status prior to commencing activity
2) Verify battery capacity or replace
3) Inspect electronics for damage, mounting integrity
4) Test to verify built in test indicators
5) Verify safe status when checks are complete
6) Prepare any non-flight critical electronics, e.g. location transmitters
E) Pyrotechnics
1) Observe safety practices prior to handling pyrotechnics
2) Test and/or inspect bridge wire (e.g. flash bulb, electric matches) items
3) Verify electronics are safed prior to connections
4) Verify electronics are safed after connections
F) Recovery system
1) Inspect all components for damage (e.g. tears, burns, cuts)
2) Inspect for tangles
3) Verify all hardware is properly secured and risers are connected
4) Pack all parachutes/risers
5) Verify heat protection (e.g. wadding, shields) is in place
6) Verify closures are properly secured
a) Install shear pins as required
b) Verify friction fits
G) Final assembly
1) Verify electronics remain in a safed condition
2) Verify igniter is available for installation (not installed)
3) Verify CG location; is it forward of the aft allowable limit?
4) Verify alignment of launch pad interfaces (if applicable)
IX) Launch checklist
A) Equipment list including
1) Ladders, step stools for loading and access
2) Standoffs
3) Special launch rails, rods
4) Launch pad tools (e.g. wrenches, allen wrenches)
5) Recovery support items, e.g. radios
B) Place model on launcher
C) Verify launch angle/trajectory
D) Install igniter
E) Arm recovery systems
1) Verify all removable items are removed
2) Verify switch locking devices or connector bayonets are engaged
3) Verify any built in test or power indications are normal for flight
4) Verify that permission exists for radio frequency usage
F) Turn on non-flight critical electronics/payloads
G) Connect igniter to launch system
H) Verify Flight Witnesses are ready
I) Indicate flight readiness to LCO/RSO
X) Post flight checklist
A) Verify all pyrotechnics are discharged
1) Safe the pyrotechnic systems if live devices are present
2) Attempt to identify the reason for the unfired pyrotechnic
B) Record or save any flight data indicates that will be lost after power removal
C) Remove power from electronic systems
XI) Contingency checklist
A) For misfires, launch aborts, or crashes
B) Safe pyrotechnic systems to allow safe handling and/or disassembly
C) Disconnect and remove motor igniter(s)
D) Note operating time to determine if flight batteries need charging or replacement
1) Include re-inspection requirements
2) Consider any other time critical items, e.g. memory storage capacity
Calculating Status Pressure Port Size
A good rule of thumb for the static pressure port is to use a 1/4" diameter hole for every 100 cubic inches in the altimeter bay compartment that is being vented. This can be described by the following equation:
A1 = V*(Aref/Vref)
where A1 is the area in square inches of a single static pressure port hole and V is the volume in cubic inches of the compartment. Aref is the area of our reference 1/4" diameter hole and Vref is our reference volume of 100 cubic inches. For example, using this equation, if V = 100 cubic inches then it cancels with Vref and leaves A = Aref, which means we need a hole with the same cross sectional area as a 1/4" diameter hole. If V = 200 cubic inches, then A1 will turn out to be twice the area of a 1/4" diameter hole. Therefore, the equation yields one 1/4" diameter hole per 100 cubic inches of volume.
The volume of the compartment can be calculated from the following equation:
V = (pi/4)*DT2*L
where DT is the inside diameter in inches of the body tube compartment and L is the length in inches of the inside of that compartment. At this point we could combine these two equations to get one equation that calculates the hole size needed for a given DT and L. However, it is not really a good idea to use just one hole. Multiple holes are better because they can help null out undesirable pressure effects caused by cross winds or unstable flight profiles. It is recommended that a minimum of three holes be used that are equally spaced around the body tube. (i.e. 120 degrees apart.) Four is also a good choice and is sometimes more convenient for physical layout.
Multiple holes can also be smaller than one hole so long as the total cross sectional area is the same. We can calculate the area of one hole from the following equation:
A1 = (pi/4)*D12
where A1 is the area of one hole and D1 is the diameter of the one hole. We can also calculate the area AN of any number of N holes of diameter DN from the following equation:
AN = N*(pi/4)*DN2
Now by combining these two equations for area, we can calculate the diameter required for the N small holes that will give the same area as one big hole. The result is:
DN = D1/sqrt(N)
where sqrt(N) is the square root of N.
We now have everything we need to combine all these equations into one final equation:
DN = DT*sqrt((Aref/Vref)*(L/N))
This equation is very useful because it directly calculates the diameter DN of the small static port holes for a compartment with body tube inside diameter DT, length L, and number of holes N. This equation can be used to directly calculate the proper hole sizes, especially in situations that do not lend themselves to the charts above.
We can also take this one step further since we know Aref and Vref. Vref = 100 cubic inches and Aref = pi*(0.25/2)2 = 0.04909 square inches.
DN = 0.02216*DT*sqrt(L/N)
Where DN is the diameter of the small static port holes for a compartment with body tube inside diameter DT, length L, and number of holes N. (All dimensions must be in inches for this equation.)
The diameter of the
altimeter bay is ~8 inches and the length is 12.5 inches or 628 cubic inches.
According to the formula, 3 ports would each be about .36
actually.
Here's the equation
provided by Missile Works for the RRC2-mini for volumes greater than 100 cubic
inches. How about four ports.
Bay Volume = radius X radius X length X 3.14
Single Vent Diameter = 2 X SQRT ( volume/6397.71))
Single Vent Radius = Single Vent Diameter / 2
Single Vent Area = ( Single Vent Diameter/2 ) X ( Single Vent Diameter/2
) X 3.14
Multi Vent Diameter = 2 * SQRT ( ( Single Vent Area / # of holes ) / 3.14)
It comes out to .31 inches for each of four ports. So 1/3" it is.
Now static vents have all kinds of possibilities.
I have two airframes and I've generally put two vents in each frame just
because. It might be a problem, but I have generally put them opposite each
other.
The lower airframe volume is `8" x 17" or 854 cubic inches
The upper airframe volume is `8" x 22" or 1130 cubic inches.
Using the static port sizing equation above.
For the lower framer that would be ~1/3 of
an inch for each of 2 holes.
For the upper airframe, that would be a
little more than 1/3 of an inch for each of 2 holes.
My plan will be 1/3" for each of the static ports. Actually, 5/16"
would probably be fine too.
Ejection Charge Sizing
The size of the required
ejection charge can be calculated based on the desired ejection pressure and
the internal "free-volume" of the rocket airframe. (The volume of the
parachute and rigging inside is neglected.) First I determined the
required pressure to separate and deploy the recovery system. This depends on
the area of the bulkhead, hence body diameter, and the mass of the nose
section. The force from the pressure must be enough to overcome the inertia and
drive the mass of the nose section the length of the coupler inside the tube to
the point of separation, plus a little more for momentum to fully deploy
everything. If you consider the nose having to deploy into a wind, or not near
apogee, you need a little more push again. Assume that the gas expands and the
pressure occurs instantly and uniformly throughout the volume. The pressure
exerts an instant force on the forward bulkhead intended for extension. Neglect
any change in pressure and temperature from the change in volume as the nose
moves forward. I'm considering a 15psi charge pressure.
Volume = Length times PI times the radius squared, or 22 x 3.14 x 3.875
x 3.875 = 1037 cubic inches.
The ejection charge equation is:
WP = (dP x V) / (R x T)
Where:
The parachute main parachute compartment is 22 inches long
with a 7.75-inch diameter (3.875" radius). The amount of powder
needed to generate 15 pounds-per-square-inch will be:
Wp = (15 x 1037) / (22.16 x 12 x 3307)
Wp = (15,555) / (879,397.4)
WP = (.0176) x 454
Wp = 8.3 grams
Wp = 128.1 grains
The Drogue Parachute Compartment:
Volume = Length times PI x the radius squared, or 17 x 3.14 x 3.875 x 3.875 =
801.5 cubic inches
The ejection charge equation is
Wp = (dP x V) / (R x T)
Wp = (15 x 801.5) / ( 879,397.4)
Wp = (12,022.5) / (879,397.4)
WP = (0.014) x 454
WP = 6.21 grams
WP = 94.14 grains
(These calculations were adapted from information posted on infoCentral. Special thanks to Ted Apke for posting it.)
The ejection charge force is calculated by multiplying the cross-sectional area of the body tube by the ejection charge pressure in psi. Divide this force by 35 pounds to get the maximum number of shear pins that can be used.
The cross section area of the parachute tube is calculated with this formula. Area = pi times the radius squared, or 3.14 x 3.875 x 3.875 = 47.15 square inches. So the maximum number of 2-56 shear pins would be calculated like this: 47.15 x 15 / 35 = 20.21. Half that number or 10 shear pins. I intend to use three 4-40 nylon screws as shear pins on the nose and two 4-40 nylon screws as shear pins at the center break point for this dual deployment.
(These calculations were adapted from information posted on infoCentral. Special thanks to Duncan McDonald for posting it.)
