Archery: Draw Weight vs Draw Force

Archery: Draw Weight vs Draw Force

Twang, thwapp! We’ve all heard this sound and know what it means, some archer has hit their mark. Bows are one of the most commonly known about items in our world despite their lack of use. We can thank characters like Legolas, Katniss, Hawkeye, or even Robin Hood for this, characters who have romanticized the bow to the extent that we all know what it is, but do we know what it can do, or how it works? I decided to set out and find this out using the physics we have learned throughout the past semester.

To first understand bows, we need to understand how they work. Bows are relatively simple constructions that, like most technology and creations, have gotten much more complicated over time. For well over 12,000 years bows have been a simple system that consists of a string attached to elastic limbs that store mechanical energy imparted by the user drawing the string. This energy would then be stretched over the string as the archer drew the bow, giving it its displacement. The elastic limbs themselves changed over time and cultures based on the materials used, traditional springy wood was preferred for its strength, and its elasticity or spryness allowed the bow to maintain its shape while in use. The arms would be produced with varying strength depending on the user, material, and would require different amounts of force to draw the bow and launch the arrow, this was then put into terms of weight giving us the term, “draw weight.”

Since then we have expanded further still on the bow and created the compound bow. The compound bow works under the same general principle as previous iterations of the bow, but is instead made from modern plastics, aluminum, and composite allows, and included pulleys, levers, and cables to enhance the draw and give a “let off point” at its max draw where the archer does not need as much force to maintain the bows draw. This type of bow also gives the strongest transference of energy to the arrow yet, normally between 70-85% of the stored energy is transferred to the arrow. This stored energy is referred to as potential energy. When transferred to the arrow it is referred to as kinetic energy. Thus I decided to test if the rate of the strength to force was the same no matter how much draw weight a bow had. I used two separate types of bows with differing draw weights, one of 15lb and one of 25lb  to see how the ratio of joules to weight ratio matched up, and if it was consistent. I hypothesized that the ratio would stay consistent no matter the draw weight of the bow as the size and power ratio should always be similar if not the same.

I then set up a target range and measured out 35 feet (10.667 meters) to use for the experiment and recorded myself launching the arrow so we would be able to accurately calculate the arrows velocity (v=distance/time) to get its force and joules. I found that the 15lb bow was able to cover the distance in .488 seconds, meaning that it had a velocity of 21.801 meters per second (48 miles per hour) and the 25lb bow was a full .1 seconds faster and went 28.074 meters per second (62 miles per hour). After plugging both of these into the kinetic energy equation (and taking into account the .076 kilogram training arrow) k=1/2 mv^2 we were able to calculate the force of each bow at 29.95 joules for the 25lb bow,(1.197 joules to pounds ratio) and 18.09 joules for the 15lb bow (1.206 Joules to pounds ratio).

Next we need to figure out the force. Using an energy bar chart we find that W=KE or work equals kinetic energy, thus our force will be equal to energy divided by the displacement, which in this case is the draw length of the bow. The 15lb bow has a draw length of .48 meters, meaning that our work equation is simply 21.801/.48, giving us 45.46 Newton’s of force (giving us a ratio of 3.03 Newton’s of force per pound of draw weight). The 25 pound bow had a .6m draw distance, making this equation 29.95/.6, or 49.9 Newton’s (a ratio of 1.996 Newton’s of force per pound of draw weight). This means that my main hypothesis of the ratio’s being relatively the same was incorrect, with a full 1.034 newton difference between them. However the two bows shared a very similar ratio of energy conservation, with only a .008 variance dependent on the quality of the bow and its size.

Thus we can see that my main hypothesis was incorrect, the larger a bow is the more its force drops off, likely due to its larger displacement causing it to have more time to loose energy, showing that a weaker bow actually has a better force to weight ratio. However we also found that both had an extremely similar ratio of energy to pound, and as a result we can consider that notable as well. Thus I will cede that I was wrong in my initial prediction, but was proven correct in a different test that shows that the total weight will always create the same amount of energy.

Possible problems

One of the most critical issues I found was my bows themselves. Both are years old, and very well used. My methods of containing them also are generally not the greatest, simply storing them in a shed in the backyard and keeping them relatively vulnerable to the cold but safe from the elements. The amount of time they have spent being used can also compromise the strength of the bow over time. For example dry firing a bow (loosening the string without an arrow in it) causes the entire energy (all 20+ joules for both bows) goes back into the bow arms from their point of weakest resistance, damaging the bow and compromising it structural integrity. I already know that this had some negative effects on the arrows themselves, as a direct weight to joules comparison places both at less force than they should, but this was much less that should worry about, as one can also consider the force loss to friction, cold, or the wind speed that could change its trajectory and time. 

Lab 13: Reflections and Mirrors

Lab 13: Reflections and Mirrors

In lab 13 we experimented mirrors to see how they reflect images and how reflection truly works. Reflections are based on how light reflects off of the reflective surface of a mirror. This causes the light to then be bounced equal arc of which some will bounce into a human eye to be perceived and viewed. This equal arc also causes the light to occupy a fixed point, and based on the mirrors position causes how we can move into and out of view of the mirror. Throughout our experiments we found that these points will be fixed and will perceive the same amount of the person no matter how far away the person is from the mirror, if it can’t see your legs at 5 ft away, it can’t see them 10-15- or even 20 ft away. As a result we were asked, what is the minimum size we can have in a mirror for it to be able to see our entire body and reflect it back at us.

To figure this out we realized that the point on the mirror that we needed to adjust was the midpoint, the area where the light bounced off of the mirror and back at us. We calculated that since the angle was always the same we could use a midpoint on our own body’s dimensions to figure out how to calculate the size. Because the rays always had to reflect to our eyes, we measured the distance from our toes to our eyes, from our shoulders to the opposite eye, and from the top of our heads to our eyes. I am personally 6'4 and had the following calculations, 182 cm toe to eyes, 8 cm top of head to eyes, and roughly 40 cm shoulder to opposite eye. We then halved this data to use their midpoint, and then added the measurements that would be used to find the mirrors dimensions, namely the head and toe points for height, and the shoulder points for width. After computing this i found that for a mirror to be properly sized for me it would need to be 95 cm tall and 40 cm wide.

Errors

As usual we did have plenty of opportunities for error. One major problem we could have had is problems measuring and rounding, as all we had was a yard stick that had to be flipped and remeasured to measure our overall height. We also had problems rounding and would commonly round to the nearest centimeter for easy use, which could provide some problems given that the dimensions needed to be exact, but a few millimeters will not make a noticeable or major difference.

Lab 12: Mechanical Waves

Lab 12: Mechanical Waves

For lab 12 we experimented with waves, specifically the mechanical waves generated by pulses. To do this we hooked a frequency generator and a mechanical wave oscillator to a string and pulled the string taunt to monitor how the frequency of the generator affected how many nodes and anti-nodes were generated. To summarize, a node is a point where the two differing waves cancel each other out and seem to have no displacement, while an anti-node is maximum point of the wave’s generated path. These points are then used to calculate the wavelength of the wave, allowing it to be measured and predicted.

 

We were tasked with finding if there was a relationship between the Node Node and Node Anti node patterns and finding out if they act the same way as the transverse standing waves? a Node Node pattern is when the wave on the string begins and ends on a node, while a Node Anti node pattern is when it starts or ends with an Anti-node and ends with the opposite. we first experimented with the transverse wave, noting the wavelength of the wave as the hertz was increased. our data was as follows.

This data showed us that the nodes and wavelengths increased as time went off, with a few outlier's until we hit 32 hertz where the total wavelengths dropped and then began to increase again. 

We then repeated the experiment with a spring instead of a rope to better measure the node patterns in them with more accuracy. We found that the nodes pattern would alternate every 5 hertz increase. As we experimented higher and higher we noticed that the number of nodes and anti-nodes would increase, this gives us the impression that the two systems are very similarity, which makes sense as they rely on the same drivers and functionality. 

Problems:

There were a few margins for error in our experiments that need to be accounted for. Firstly our equipment had occasional problems achieving the correct speed, leading to some puzzling readings which are why we do not have any data pictures for the second part. Additionally we have the traditional human error problems for input, and may have added in unknown outside problems due to treatment of the machines or how they were placed.

Lab 11: Electromagnetic Induction

 For lab 11 we experimented with electromagnetic induction using a Magnet, coils with varying number of windings, a galvanometer, a power supply, and connecting wires. We were tasked with influencing the magnitude of the inducting current, shown on the galvanometer. To do this we first experimented by hooking a magnetic coil to a galvanometer and ran a magnet through the coil, alternating its sides and monitoring the galvanometer. We found that running the magnets through the coil would cause the galvanometer to register an increase when the north side was run through the coil and a decrease when it left, while the opposite was true when the south side went through it. This was due to the magnetic field that the magnet possessed, which changed to the coils electric current causing the changes.

Next we experimented with the voltage of the coil. We hooked a power supply to the coil and experimented with changing the voltage run through the coil. We found that increase the voltage decreased the current, and again the inverse caused it to increase. This was caused due to the coils current working to compensate and equalize for the voltage to equalize its magnetic field.

Next we experimented with a second coil, we added a second coil to the first and linked the two but did not link the second to the power supply. This caused the reverse effect of the previous experiment, with the second coil equalizing the first and thus causing it to increase its magnetic field to compensate.

Finally we repeated the previous experiment but with a magnet, in this occasion we found that the second coil had the reverse reaction to the first, noting that it’s current would increase with the south side of the magnet and decrease with the north.

from these experiments we were able to note that many things increase the coils magnetic field, the facing of a magnet that is brought into it, reducing the voltage introduced to the coil, and the introduction of a second coil that will experience a reverse version of all of the different ways that we attempt to influence the magnetic field with. Thus there are a large amount of things that can influence a coils magnetic field, and in many ways.

Lab 10: Magnetism

Lab 10: Magnetism

In Lab 10 we experimented with magnetic fields, studying how they acted and where they were directed between a magnets north and South Pole. During this experiment we measured our first 3 dimensional object that was large enough to interact with, a Helmholtz coil.

   

We were tasked with measuring it’s magnetic field lines to find where they went and isolate its north and south poles. to do this we took a compass and a sheet of paper to track the needles direction and began moving the compass in differing areas of the coil, marking the needles facing on the sheet of paper every roughly 30 degrees. Doing this we noticed that the field seems to move as shown below.

This showed us the main movement and area of the coils magnetic fields, and how similar they could be. The coil has a single moving line going through its center as a result of the cancelling effects of the different fields on either side of the center, creating a uniform and regular magnetic field that can be easily modified.

Possible flaws

due to our only measuring every 30 degrees we could have possibility missed or failed to gain the fields size due to measurement or user error, additionally as we could not directly trace it very well on the sheet of paper we were unable to guarantee that it was correct, a better way to possibly perform this experiment in the future would be with metallic dust that we could track and monitor to see how it moved in relation with the magnetic fields, but that could end up being too much of a mess to clean up to be worth using.

Lab 9: circuits

Lab: 9 circuits

To experiment with and learn more about circuits we hooked up an ammeter to a power source and began experimenting with how resistors, light bulbs, and changing the amount of resistors affected the voltage going through the wires. After experimenting with a light bulb we measured the voltage of the wire after it had gone through the light bulb and found that voltage seemed to increase linearly with the amps, or as we increased the power the brighter the light bulb seemed to get, logically this made sense. Thus we made the argument that all of the system would follow the same principle.

This however proved untrue when we added in a second resistor. After adding a second resistor we found that the voltage began to experience an exponential growth. This seemed to be based on how and when the resistors began absorbing the charge and how much began to go through at a time. As the amps increased the voltage being stopped and regulated by the resistors seemed to be mixed up by the second resistor, changing the voltage increase from a linear one to an exponential one.

Thus our original prediction was proven false, the information managed to both contradict and support our original experiment. The voltage in the current did increase based on the amps provided, but were limited in differing amounts based on the amount of resistors in the wiring.

Problems and issues

an unfortunate problem we had was that the voltage would change roughly based on how much pressure and where we placed the attaching clamps on the resistor or how tightly we held the wires to the light bulb. this could have disrupted some of out data an information, but not likely enough to disrupt the entire results.

Lab 8: Electrostatics

Lab 8: Electrostatics

There are many ways to test Electrostatics, but some of the best ways to test and explain them is through Pith balls and electroscopes. Pith balls are two lightweight “pith” balls suspended from the strings are attracted to objects with a static electric charge. The pith balls can also be charged by touching them to an object with a static electric charge. 

                                                           

Electroscopes are device used to detect the presence of charge and its relative amount. They are usually constructed with a metal plate or sphere at the top of a metal post with a metal rod hanging from the bottom of the post.

                                                             

These two are charged with differing charges making them very reactive to differing electrical energy and charges that come near to them. This can be caused by the movement of the electrons within the instrument which cause the lighter materials in the instrument to move towards or away a grounded rod that is brought close to it. These instruments will react differently but can be easily understood. We experimented with this in class by grounding several rods with alternating charges and touching and moving the rod around the instruments to see how they react. This can be used to discover the charge of the object by checking how the instruments react, if they are opposite to the object then balls will be attracted to each other and move towards each other, while if they are similar to each other they will be pushed away from each other. In turn an electroscope will move when an electrically charged and grounded object moves near it and will actually stay in an elevated position due to the electrons being transferred to the electroscope through the contact. 

These two instruments are effective at serving as an effective way to test objects in their own way, pith balls can show whether an object has a positive or negative charge, while a electroscope can show the strength of the charge by how it stays up when charged. Thus these instruments are very useful when testing for and find unknown charges.

Lab 6: Energy part one

Lab 6: Energy part 1

To experiment with work and how it affects the energy, velocity, and movement of an object. To do this we set up a friction less track with a slider and weights and began alternating the height and placement of the slider on the track. We would then change the amount of force we exerted on the cart and monitor how fast it traveled a see how that affected the work done. We recorded this information into logger pro, here is an example of the difference between a forceful shove and actually fighting the weights to let the cart fall slower.

The data was partially conclusive with our initial prediction, that more force would move the track faster, but this did not vastly change the integral, averaging on a few 10ths of a joule where a joule is equal to Mass*Newton’s like we had thought it would. 

To expand on this we set the track up as a ramp to test out and see if height or displacement would have any effect on the integral. We varied our height by about 20cm by first testing the slider from 70 cm to 190, and then from 90cm to 190cm. our results are below, and served to concur with our prediction.

We then elevated to track and increased the incline of the ramp and used the same two distance markers.  The heights were different at the same points along the ramp at 90 cm (8.8 cm vs. 10.2 cm).  We compared the integrals and found that height does matter= .3243J vs .2074J for the first trial at a lower incline, as shown here.

These experiments show us that height matters when it comes to work being done.  Potential energy is higher when the incline is higher.  Varying force seems to not affect the work when the distance (displacement) is the same.  This all ties into work done in order to change energy in a system.

Possible issues.

One of the greatest issues we had with the experiment was ensuring that the track stopped smoothly. With such a short track we were forced to abandon several graphs due to this problem as the tracks would flip backwards and disrupt the information, making the graph useless and corrupting the integral measurement. 

Lab 5: Circular motion

Lab 5: Circular motion 

For lab 5 we were asked to find the mass of an object spinning in a circular motion. In order to properly test this we used the DMV Player program Motion in a circle.

To first calculate the mass we needed to find the object velocity.  We set the graph to 30 FPS and monitored the simulation to see how long the graph would take to send the object in a complete circle. We calculated it to take 724 frames to complete its rotation, thus meaning it took 24 seconds to complete its circle. 

The simulation then provided us with the force of the movement up in the top center. We were then able to calculate the velocity of the object by using the rotation motion equation, v=2piR/time, or plugging the numbers into it v=2pi60/3.016, giving us a velocity of 1.25 centimeters. 

We are then able to calculate the acceleration using velocity/radius to get an acceleration of 2.6 MPS. We were then able to plug this into the traditional force formula, F=MA, or in this case 1.15=m*2.6, which we can divide our acceleration into the force for 1.15/2.6=M, or .44Kg of mass for the object.

Errors

Possible errors that could change our results were rounding errors, improper conversions between centimeters and meters.

Lab 4

For lab 4 we were asked to find the initial acceleration of an elevator when it starts and stops. To do this we were given a force probe attached a 550 gram weight and stand that would measure the change in force as the elevator accelerated. 

Before we could do this we had to first calculate the amount of force that gravity was putting on the probe itself in order to subtract it from our findings in the elevator. After zeroing the probe we found that gravity placed roughly 5.1 newton’s of force on the probe, with this information in hand we quickly sketched a set of a motion diagram, force diagram, and force addition diagram. We calculated that the elevator would have its forces cancelled out by both the tension in the cable and the force of gravity until the moment of acceleration, at which point the motor in top of the elevator shaft would either increase tension to make the elevator go up or decrease it to make it stop and equalize. We would then be able to calculate the elevators acceleration by dividing the change in force by the velocity, giving us the acceleration.

Armed with this information we proceeded to the elevator and took a single reading from the start of the elevators trip to the bottom to its stop at the bottom floor that provided the following chart from logger pro.

From this information we were able to discover the force at the time of acceleration at the elevators beginning and ending. Logger pro calculated the force at approximately 5.1 at the beginning as the elevator traveled downwards and increased to 5.8 at its stop in order to counteract its velocity downwards and 5.3 for its constant movement. We then subtracted the constant force of gravity, 5.1 from each reading to find the change in force, calculating to -.3 net force for the initial downwards acceleration and a .4 increase for the upwards acceleration to cease moving and a constant .2 difference. 

We then plugged this information into the formula Weight*Acceleration=Force, giving us 550*A=5.1, which after dividing the force by the weight to isolate acceleration gave us 0.009 Meters per second for start, and then did the same for its acceleration to stop, calculating to 0.010, keeping the force relatively the same for the elevator. To calculate the speed of the elevator we divided this number by the weight of the weight attached to the recorder in kilograms, calculating that the average speed of the elevator was .36 Meters per second. A fairly comfortable pace for an elevator that takes roughly 9 seconds to go between floors.

Possible problems.

Gaining the information for an elevator is not always exact as it can be difficult to time the movement of the elevator with when the graph starts and ends, we were lucky, but we may have missed some critical data. Additionally we always needed to take the averages of the information and that can sometimes be skewed by large temporary readings, like the short hikes that the graph shows for the initial movements of the elevator.

Lab 3: Forces

For lab 3 we experimented with forces and motion and how they could affect and change the acceleration and velocity of an object. The final result of this was an experiment that monitored the change in velocity as more weights were added to double the amount of force being used to pull the slide, as can be seen below. In order to create a controlled and uncontrolled system to compare the results to we used compressed air to create a friction-less environment and then used the rail base to compare how friction can change an objects velocity.

To support these findings we also experimented with changing and varying the amount of newtons to pull a car and see how its acceleration changed, seeing that the value increase with the amount of force applied.

 

These experiments tied into the very first experiment we did where we experimented with changing the location and amounts of force exerted on a bowling ball to see how we could influence it. constant force would create constant acceleration while when provided with a much more loose or reduced friction environment, or constantly maintained force to produce a constant velocity. The secondary experiments supported this with the first one providing an example of changing force and the second and example of constant force, supporting the statement that all motion is based on the force behind it.

Lab 2, APPLICATION EXPERIMENT: WHAT KIND OF MOTION?

For lab 2 we were assigned to find whether a provided coffee filter would fall at a constant speed,
constant acceleration, or changing acceleration. In order to do this we decided to place a motion detector on the floor and align said coffee filter with the reader above it and drop it onto the motion detector. After several tries that caused the filter to drift off of the scanner and disturb our results we elected to place several filters together in order to give the object more mass and allow it to fall straighter without being disturbed by passing persons or air currents. The result of this can be found below.

Our results were then recorded and we compared the slope of the graph to calculate its constant rate of motion to determine its rate of motion and if that rate changed or was constant, representing whether its fell constant speed, constant acceleration, or changing acceleration.

We began with an over view of the movement.

As can be seen on the graph the coffee filter slowly begins to accelerate in its constant motion due to its increase in its acceleration downwards. this rules out the question of whether the filter falls at constant speed.

In these next two we can see that the velocity and position are constantly changing, by definition ruling out the possibility of constant acceleration as the rate is not constant, rather changing. Thus we can surmise that the coffee filter falls with a changing acceleration until it hits the floor, at which point it achieves a quite constant and unchanging acceleration of zero as it is resting in place.

Problems;

While we did the best we could we acknowledge that there are some problems with this form of measurement. Firstly the most common problem was that the filter was too light and had a tendency to drift off the scanner, invalidating our readings, this can be caused by a simple drift to the right or even a person walking by and disturbing the air. Additionally we were dropping the filter from a height of roughly one meter, a height that serves well as a basis for a smaller measurement but does not allow for terminal velocity to take effect, possibly changing the experiment.