I apologize for contributing to a topic that has brought so much anguish to others, but I’ve done some speculative calculations on the specifications of the Vulcan. Before I start addressing specific questions, I’d like to add a disclaimer that these calculations are done under ideal conditions for simplicity (friction, air loss, air resistance, weight of certain components are negligible, etc.) and with assumptions on the performance of the Vulcan. Among these assumptions are as follows.
1. The Vulcan priming mechanism is based on an airsoft AEG.
2. Mass of an average NERF or modified dart is 10 grams.
3. Radius of an average NERF or modified dart is 0.005 m = 0.5 cm = about 1/4 inches.
4. Gear is made of nylon engineering plastic (Wikipedia: density = 1.15 g/cm^3).
5. Radius of the gear is 1.5 cm = 0.015 m and 1.0 cm thick.
6. Mass of the gear is roughly 8 grams = 0.008 kg. (Calculated from assumptions 4 & 5)
7. Only 1 gear is used.
8. Dart falls 1 meter after traveling 9 meters (~30 feet)
9. The Vulcan’s pull length is 3 inches (0.0762 m).
10. The Vulcan pull length is the spring compression length.
11. A springer plunger works like an ideal mechanical piston.
Certain figures are also rounded, and calculations are non-integrative (no background in Calculus required, only physics).So what do we know:
Shots per second = 3.5 (calculated by Secran)
Energy source = 6 x 1.5V D cell batteries in series = 9VWhat I’ve speculated out:Volume of air used:
Chamber volume = (Cross-sectional area of dart) x (pull length)
= (pi)(0.005 m)^2 x (0.0762 m)
= 5.98 x 10^-6 cubic metersWork per shot (dynamic change of pressure discounted):
Work per shot = (chamber/atmospheric pressure) x (volume displaced)
= (101325 Pa) x (5.98 x 10^-6 cubic meters)
= 0.606 JWork per second (Power):
Work per second = (work per shot) x (shots per second)
= (0.606 J/shot) x (3.5 shots/s)
= 2.121 J/sMuzzle velocity (acceleration of the dart in the barrel is discounted):
0.5 x (mass of dart) x (muzzle velocity)^2 = work per shot
muzzle velocity = 2 x (work per shot) / (mass of dart)
muzzle velocity = [2 x (2.121 J/s) / (0.01 kg)]^(1/2)
muzzle velocity = 20.596 m/s = 46.07 mph
OR kinematically, under assumption 8,
(drop height) = 0.5 x (acceleration due to gravity) x (time of flight)^2
(time of flight) = [2 x (drop height) / (acceleration due to gravity)]^(1/2)
= [2 x (1 m) / (9.8 m/(s^2))]^(1/2)
(time of flight) = 0.452 s
muzzle velocity = (distance traveled) / (time of flight)
= (9 m) / (0.452s)
= 19.9 m / s = 44.5 mph
The speeds are relatively close, so my assumption on the figures and range are nearly accurate.Revolution speed:
The electrical work done by the motor in a loss-less system should equal the rotation energy of the gear.
Work per shot = (0.5) x (moment of inertia of gear) x (revolution speed in rad/s)^2
Revolution speed = [2 x (work per shot) / (moment of inertia of gear)]^(1/2)
Revolution speed = [[2 x (work per shot) / [0.5 x (mass of gear) x (radius of gear)^2]]^(1/2)
Revolution speed = [2 x (2.121 J) / [0.5 x (0.008 kg) x (0.015 m)^2]]^(1/2)
Revolution speed = 2171 radians/second
Revolution speed/(2 x pi) = 345.53 rpm = 5.76 rpsCocking time:
Cocking time = (pull length) / [(revolution speed in rps) x (circumference of gear)]
Cocking time = (0.0762 m) / [(5.76 revolution/second) x (2 x pi x (radius of gear))]
Cocking time = (0.0762 m) / [(5.76 revolution/second) x (2 x pi x (0.015m))]
Cocking time = 0.14 secondsPlunger travel time
= (1/3.5 seconds/shot) – Cocking time = 0.1457 secondsElectrical Current of Motor:
Current = (Power) / (Voltage)
Current = (2.121 J/s) / (9 V)
Current = 0.235 A or roughly 0.25 A
Notes: This current rating is somewhat idealistic. I think 1 A might be more realistic.Spring constant:
Work per shot = 0.5 x (spring constant) x (plunger length)^2
Spring constant = 2 x (work per shot) / (plunger length)^2
Spring constant = 2 x (2.121 J/s) / (0.0762 m)^2
Spring constant = 730.57 N/m = 4.17 lbs/inch
It seems battery life and cost per shot is a major concern among nerfers, so everything pertaining to that subject is summarized here. Keep in mind that the data on battery life is very speculative. At some point, voltage will decrease significantly in the battery and become useless. You might be very lucky to even attain half the shots estimated here. All values are taken from http://www.andybaird.../batteries.html
.Shots per 6 batteries (with estimated current of 0.25A):
Shots per 6 batteries = (battery life in hours) x (shots per second) x (3600 seconds per hour)Alkaline*: 20160 shots
Lithium*: 100800 shots
NiMH: 37800 - 63000 shots
NiCd: 25200 shots
Alkaline Rechargeable: 12096 shotsCost per shot (with estimated current of 0.25A):
Cost per shot = 6 batteries x (cost per battery) / (shots per 6 batteries) Alkaline*: 0.0074 – 0.0223 cents
Lithium*: 0.00893 – 0.021 cents
NiMH: 0.0214 – 0.091 cents
NiCd: 0.06 cents
Alkaline Rechargeable: 0.087 – 0.149 centsShots per 6 batteries (with probable current of 1A):Alkaline*: 5040 shots
Lithium*: 25200 shots
NiMH: 9450 -15750 shots
NiCd: 6300 shots
Alkaline Rechargeable: 3024 shotsCost per shot (with probable current of 1A):Alkaline*: 0.030 – 0.089 cents
Lithium*: 0.0357 – 0.0833 cents
NiMH: 0.0857 – 0.365 cents
NiCd: 0.238 cents
Alkaline Rechargeable: 0.3472 – 0.595 cents
** Prices are U.S. cents.
What seems really skeptical for me is the cocking time because it’s about as quick as the plunger travel time. I would think that the plunger travel time should be significantly faster. This is probably due to the fact that the calculations of the time are done using arbitrary dimensions for the gear. The battery life in terms of shots seems to be really high as well, even at the probable 1A setting. It’s likely, however, that the effective battery life will be much shorter. Because the “work per shot” figure was used to calculate the “shots per 6 batteries” figure, the work per shot figure and the power figure are also suspect. I think the only reliable figure I would stick to my guns on would be the muzzle velocity and range figures. They seem pretty nerf to me. Same with the spring constant.
Again this is all theory and ultra-simplified. If anyone has any actual experience on this or notices any mistakes/major issues to address, please give me some feedback.
Unit conversions were done using the applets at http://www.digitaldutch.com