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Impact Comparison Test 2

Results

Discussion

Conclusion

Calculation Aim

To compare the impact of water rockets with the impact of bolts fired from an SCA legal ballista.

Method

The pendulum constructed for the first impact comparison test was used.

Ballista bolts and water rockets were fired at the pendulum target until 5 direct hits were scored. The deflection of the pendulum cased by each hit was measured between the top of the target and the equivalent position on the pointer.

Arrows were also fired into the pendulum 5 times as a means of comparing the behavior of the pendulum with the earlier tests.

Ballista ready to fire.

Cannon ready to fire

Ballista Bolt and Water Rockets Specifications

Details of Water Rocket Construction

Details of Ballista Bolt Construction

The heads and fins were fixed to the shafts / bottles with duct tape.

Ballista Bolt

Water Rocket

Mass:368 g (13 oz)

Mass:144 g (5 oz)

Length:58.5 cm (23 in)

Length:31.5 cm (12.5 in)

Notes

The arrow used was a Lochac standard war arrow. It was constructed with a 28 in cedar shaft taped with glass fibre tape, a Lochac blunt and plastic nock and fletching.

The arrow was fired from a modern laminate recurve bow with a draw weight of 30 lb at a 28 in draw.

The 600 ml capacity water rockets were half filled with water and the remaining volume pressurised to 100 PSI before firing.

All test took place at a range of 5 meters (15 feet).

Aim / Method

Discussion

Conclusion

Calculation Results

The results of the trials, in the order they were recorded, are listed below.

Missile Deflection (cm)
Average (cm)

Standard Deviation

Arrow 15, 16, 18, 16, 17
16.4

1.1

Ballista* 71, 67, 69, 68, 67
68.4

1.7

Water Rocket 48, 41, 45, 43, 39
43.2

3.5

*To enable measurements of the impact of the ballista an extra 1.1 kg (2 lb 6 oz) was added to the pendulum in the form of a G clamp.

To enable the comparison of these results with potential future tests performed by other parties the average work done on the pendulum by each missile has been calculated. For information on how these results were arrived at see the calculation section.

Rocket

Ballista

Energy Transferred (joules)
3.5

16.6

Short MPEG clips showing an example trial for each missile can be downloaded by clicking on the stills below.

Rocket

Ballista

Ballista with extra weight on pendulum

Aim / Method

Results

Conclusion

Calculation Discussion

The term 'SCA Legal' as it is applied to the ballista refers to the weight of its projectile being under 1 pound and its maximum range being less than 80 yards. It does not specifically refer to the constriction of the ballista or the means it uses to generate power (elastic cords as opposed to torsion).

The average deflection caused by the arrows in this trial (16.4 cm) is close enough to the deflection caused by the same arrows in the previous trial (17.0 cm) ( impact comparison test ) to allow a meaningful comparison between the results of both trials.

The first impact of the ballista with the pendulum pushed it in a circle completely around its pivot. Since making a measurement of deflection under those circumstances was impossible extra weight, in the form of a G clamp, was added. The extra weight and its effect on the center of balance of the pendulum was taken into account when calculating the force.

The only significant difference in the construction of the rocket used in this and the previous trials was the inclusion of a layer of closed cell foam on either side of the wooden disk. Since the mass difference between the two rockets is negligible it seems that the nearly forty percent reduction in the amount of impact transferred by the rocket in this trial can be largely attributed to the foam disks.

Conclusion

The water rocket tested in this trial imparts an average impact that is less than one quater of the impact imparted by bolts fired from an SCA legal ballista.

Aim / Method

Results

Discussion Calculation

When the pendulum reaches its highest point after an impact it's potential energy is equivalent to the kinetic energy transferred to it by the missile.

The potential energy of the pendulum is given by

u = mgh

where

u = potential energy
m = the mass of the pendulum
g = the force of gravity
h = the height of the pendulums center of mass above its resting point (equivalent to the length EF in the diagram opposite)

From the length of the pendulum at which the displacement AB is measured and the length of the displacement BC the magnitude of the angle a can be calculated using the formula for the length of a chord where AB is the radius and BC is the chord length.

Since ABC has the same proportions as ADE the length DF is equal to BC * AD / AB.

Because ADE is an isosceles triangle b = (180 - a) / 2. b and d comprise a right angle so d = 90 - b.

Knowing the length of DF and the magnitude d of allows the calculation of EF by use of the sin rule.

From EF and the mass of the pendulum the amount of energy transferred to the pendulum can be calculated by use of the formula u = mgh.

Pendulum Properties

Length of pendulum at which displacement is measured AB 52 cm (20.5 in)

Length to the pendulum's center of mass AD 38 cm (15 in)

Mass of pendulum 2.75 kg (6 lb)

Pendulum Properties - with G clamp attached

Length of pendulum at which displacement is measured AB 52 cm (20.5 in)

Length to the pendulum's center of mass AD 51 cm (20 in)

Mass of pendulum 3.85 kg (8 lb 6 oz)

Results of calculation steps

Rocket

Ballista

Average Measured displacement BC(cm)
43.2

68.4

Displacement of center of mass DF(cm)
31.6

67.8

Vertical displacement of center of mass EF(cm)
13.1

44.1

a(degrees)
49.1

82.2

b(degrees)
65.5

48.9

d(degrees)
24.5

41.1

Potential energy (joules)
3.5

16.6

Back to Water Rocket Safety



Results Discussion Conclusion Calculation	Aim To compare the impact of water rockets with the impact of bolts fired from an SCA legal ballista.

	Method The pendulum constructed for the first impact comparison test was used. Ballista bolts and water rockets were fired at the pendulum target until 5 direct hits were scored. The deflection of the pendulum cased by each hit was measured between the top of the target and the equivalent position on the pointer. Arrows were also fired into the pendulum 5 times as a means of comparing the behavior of the pendulum with the earlier tests.


	Ballista ready to fire.	Cannon ready to fire

	Ballista Bolt and Water Rockets Specifications

	Details of Water Rocket Construction



	Details of Ballista Bolt Construction



	The heads and fins were fixed to the shafts / bottles with duct tape.



	Ballista Bolt		Water Rocket
	Mass:368 g (13 oz)		Mass:144 g (5 oz)
	Length:58.5 cm (23 in)		Length:31.5 cm (12.5 in)

	Notes The arrow used was a Lochac standard war arrow. It was constructed with a 28 in cedar shaft taped with glass fibre tape, a Lochac blunt and plastic nock and fletching. The arrow was fired from a modern laminate recurve bow with a draw weight of 30 lb at a 28 in draw. The 600 ml capacity water rockets were half filled with water and the remaining volume pressurised to 100 PSI before firing. All test took place at a range of 5 meters (15 feet).

Short MPEG clips showing an example trial for each missile can be downloaded by clicking on the stills below.



Rocket	Ballista	Ballista with extra weight on pendulum



Aim / Method Results Conclusion Calculation	Discussion The term 'SCA Legal' as it is applied to the ballista refers to the weight of its projectile being under 1 pound and its maximum range being less than 80 yards. It does not specifically refer to the constriction of the ballista or the means it uses to generate power (elastic cords as opposed to torsion). The average deflection caused by the arrows in this trial (16.4 cm) is close enough to the deflection caused by the same arrows in the previous trial (17.0 cm) ( impact comparison test ) to allow a meaningful comparison between the results of both trials. The first impact of the ballista with the pendulum pushed it in a circle completely around its pivot. Since making a measurement of deflection under those circumstances was impossible extra weight, in the form of a G clamp, was added. The extra weight and its effect on the center of balance of the pendulum was taken into account when calculating the force. The only significant difference in the construction of the rocket used in this and the previous trials was the inclusion of a layer of closed cell foam on either side of the wooden disk. Since the mass difference between the two rockets is negligible it seems that the nearly forty percent reduction in the amount of impact transferred by the rocket in this trial can be largely attributed to the foam disks.