what is the best ratio of payload mass to counterweight mass in a tebuchet

April 09, 2022 Post a Comment

The Optimum Arm Ratio of a Trebuchet

Kyle Carpenter

David Torbeck

Tabular array of Contents .:. Return to research

Background
Question
Literary Connectedness
Hypothesis
Materials
Procedure
Information Collection
Data Analysis
Conclusion
Pictures
Bibliography

Groundwork

Outset used in Ancient China with men pulling every bit a counterweight in a crude pattern, trebuchets traveled across the silk road to the Middle Eastward and eventually Europe to be used as a very constructive siege engine. There they reigned for 200 years as the main fashion to suspension downwards a castle wall until the advent of gunpowder weapons. A siege engineer that could build a trebuchet was of corking value to whatsoever king as information technology took precise calculations and handiwork to build not simply a functioning trebuchet but 1 that could knock a hole into a wall from a certain altitude.

Composed mainly of woods with metal supports and either a counterweight made of dead weight (usually lead) or a box for which the weight could be altered, the thought backside the trebuchet was that the counterweight could bring the projectile total circumvolve for a greater arc and therefore a greater throwing distance and forcefulness. Also, calculation wheels could farther stabilize the siege machine and enhance the throwing distance of the projectile.

Trebuchets were a mainstay of the medieval army and proceed on as a symbol of medieval siege warfare.

Question

How does the arm ratio on a trebuchet affect it�s horizontal velocity?

Literary Connection

There are lots of dissimilar variables that we could change on our trebuchet, only nosotros chose the ratio between the counterweight arm and the throwing arm. So nosotros will be measuring the horizontal velocity of the projectile as a result of the arm ratio. The optimum arm ratio has factors similar beam mass and counterweight mass, as well equally beam shape (One thousand Denny). The trick to finding an optimum arm ratio is to balance the leverage with the speed of the throwing arm (ripcord.ws). Dan Becker suggests that the optimum arm ratio is 4to 1 or greater. Philip Radlinski explains that equally the size of the throwing arm increases, the altitude the projectile is thrown increases then rapidly decreases. This means that the shape of the graphed results will most probable exist an inverse parabola.

Hypothesis

If the distance thrown is dependent on both the leverage of the counterweight arm and the speed of the throwing arm, so our data will resemble an inverted parabola with a tiptop at the ratio of five:1 because as the counterweight arm gets shorter, the force will subtract due to being so close to the fulcrum, and equally the throwing arm gets shorter, the force volition increase due to being so far from the fulcrum.

Materials

� Trebuchet with variable arm ratios

� Meter tape

� Finish sentry

� one pound solid projectile

Procedures for testing the trebuchet

1. Ready the trebuchet

2. Set out a meter tape starting from the front end of the base of operations and lay on ground

3. Move the arm to position 1

4. Load the trebuchet

v. Launch the trebuchet

6. While the trebuchet is bieng launched, fourth dimension the throw from when the projectile leaves the sling to when it hits the basis

7. Record the distance and time on a piece of newspaper

viii. Repeat steps four � seven to get two more trials on this arm ratio setting

9. Repeat steps iv � eight for all ten settings

10. Clean information technology all up

Data Collection

Position	Ratio	Altitude	Time	Velocity	Distance	Fourth dimension	Velocity	Distance	Time	Velocity
Position	Ratio	Launch 1			Launch two			Launch three
ane	v.7	12.7	2.six	5.0	15.8	2.seven	v.viii	18.3	2.7	six.9
ii	five.0	21.9	3.1	7.two	24.9	three.0	8.ii	28.5	3.1	9.3
three	iv.five	37.7	3.3	eleven.v	40.4	3.2	12.half dozen	35.3	3.3	10.vi
4	four.0	43.2	3.4	12.8	45.0	three.5	xiii.0	41.8	3.7	11.4
five	three.half dozen	49.0	iii.5	xiii.nine	54.1	iii.5	15.3	51.five	three.5	fourteen.8
6	three.iii	57.eight	3.half dozen	fifteen.9	61.0	three.8	16.1	52.3	3.0	17.iii
7	3.0	63.v	3.7	17.iii	61.0	3.8	16.3	58.viii	3.iv	17.2
8	2.8	61.0	iii.6	17.2	55.8	3.8	14.vii	57.1	3.6	15.8
9	2.5	54.three	3.4	xvi.two	57.7	three.8	fifteen.one	53.0	3.9	13.8
10	2.three	49.0	4.0	12.4	forty.3	three.9	10.3	43.0	3.viii	eleven.3

Information File (Text) (Excel)

Data Assay

Decision

Our hypothesis was not supported because the optimum arm ratio seemed to be 3:i and non 5:1. This happened considering at 5:1, in that location was non enough power to lift the arm and the projectile and nevertheless take enough free energy to throw the projectile at a high velocity. On the other paw, at the three:i ratio there was but the correct balance betwixt leverage and speed of the arm to achieve the highest velocity. Some errors that nosotros might have had in our experiment include, wind, measuring, and the axel connection. The wind could have caused us errors by blowing our projectile off to one side, pushing it frontwards, or pushing information technology backwards. Some errors that nosotros had in measuring could accept happened because we laid the meter record on the basis in a stationary position and no matter how far to the side of the tape the projectile landed, nosotros just looked at the meter tape and guessed the distance. Some other fault in measurements that we had was in the timing. The person who was timing started the watch when the projectile was released and stopped it when it landed, which could accept been 60 M away. With starting and stopping points this uncertain, there could have been many timing errors. Another mistake that could have occurred was the axle connection. Because nosotros drilled the holes for our get-go axle and had to change the beam when the first one that we made broke, the connection between the new beam and the arm was loose and sometimes sliding around. To set up these errors, we could test information technology on a less windy 24-hour interval, be more conscientious timing, and drill the holes for the smaller axle in the beginning place.