Free fall is motion with no acceleration other than that provided by gravity

“Free fall is motion with no acceleration other than that provided by gravity. This also applies to objects in orbit, even though these objects are not "falling" in the usual sense of the word” (“Physics:physics…). Strictly speaking, nothing falling through an atmosphere can be in free fall due to the inherent resistance to motion; however, in skydiving, the term is also applied to the period of the jump before the parachute is opened, and in colloquial usage, falling through an atmosphere is normally considered to be free fall. Examples of objects in free fall include: A spacecraft (in space) with its rockets off, the moon orbiting around the Earth. An object dropped in a vacuum tube - for a physics demonstration. Examples of objects not in free fall: Standing on the ground: the gravitational acceleration is counteracted by the reaction force from the ground. Flying horizontally in an airplane: the wings' lift is also providing acceleration. Jumping from an airplane: there is a resistance force provided by the atmosphere. Near sea level, an object in free fall in a vacuum will accelerate at approximately 9.8 m/s $2$ , regardless of its mass. With air resistance acting upon an object that has been dropped, the object will eventually reach a terminal velocity (around 120 mph (200 km/h) for a human body). An object that is falling through the atmosphere is subjected to two external forces. One force is the gravitational force, expressed as the weight of the object. The other force is the air resistance, or drag of the object. “The motion of any object can be described by Newton's second law of motion, force F equals mass m times acceleration a”: F = m * a, which can be solved for the acceleration of the object in terms of the net external force and the mass of the object: a = F / m (“Newton’s law of…”). Weight and drag are forces which are vector quantities. The net external force F is then equal to the difference of the weight W and the drag D: F = W – D. The acceleration of a falling object then becomes: a = (W - D) / m. The magnitude of the drag is given by the drag equation. Drag D depends on a drag coefficient Cd, the atmospheric density r, the square of the air velocity V, and some reference area A of the object.

During a skydive jump, a skydiver undergoes many different experiences. The freefall and the parachute ride are actually divided up into subcategories that enable a skydive to be completely and accurately analyzed. The freefall consists of the reaching of terminal velocity and falling at terminal velocity for a certain amount of time. The parachute consists of the deployment of the parachute - its mass deceleration and its effects on the human body, and the actual parachute ride which has to be at a “safe for landing” velocity.

Method ▲

One could say that the “setup” for our investigation could be divided into two parts. The first involves Tylden’s skydiving experience earlier on in the year. Without it, it is highly probable that our project wouldn’t have developed. Thus, the parachute, suit, plane, various other pieces of equipment and field in Eugene that all went in to Tylden’s dive could be considered our “setup #1”. Setup #2, or the analysis phase of our project, included several computer programs and various complex equations. We began our project by modeling the sky diving experience using a simulation program called Interactive Physics.

Afterwards, we analyzed the various theories related to skydiving that we had collected earlier using SUVAT equations. The decreased acceleration part of our project called for the use of a calculus formula involving mass and viscosity of air. Its solution illustrated to us the acceleration, velocity and position of a skydiver at any given time. Combining this formula with one that focuses on the x-axis, we were able to compare the vertical position to the horizontal position of a skydiver. This showed us the most probable trajectory of a skydiver.

Several factors influenced the way we approached this project. We found ourselves often accommodating for lack of certain resources. For example, we could have potentially measured the acceleration of a skydiver by hooking Tylden up with a Vernier accelerometer when he went skydiving. Unfortunately, getting our hands on one turned out to be harder than we thought. We later decided though that using one would have been risky, considering one would only have one chance to collect data. Our method also proved to be less expensive than others would have been.

Results ▲

The uncertainty in the experiment is initially found in the theories that are being tested. i.e. There are arguments between whether the terminal velocity of a person is 190km/h or 200km/h, however the majority of the sources agree with the first mentioned. The below mentioned data is a complete SUVAT of the entire Skydiving experience, subdivided into specific categories and as a combined average. There is a SUVAT for Accelerated freefall, constant freefall, net freefall, parachute deployment, parachute floating, net parachute and net jump. There is a SUVAT in both x axis and y axis.

	accelerated freefall
	x	units	other	units	other	units	other	units
s	2264.80	m	2.26	km	1.42	mi	7473.84	ft
u	250.00	m/s	900.00	km/h	559.23	mi/h	820.21	ft/s
v	101.00	m/s	363.60	km/h	225.93	mi/h	331.36	ft/s
a	-9.80	m/s/s
t	15.20	s

	constant freefall
	x	units	other	units	other	units	other	units
s	821.40	m	0.82	km	0.51	mi	2710.62	ft
u	101.00	m/s	363.60	km/h	225.93	mi/h	331.36	ft/s
v	10.00	m/s	36.00	km/h	22.37	mi/h	32.81	ft/s
a	-6.15	m/s/s
t	14.80	s

	net freefall
	x	units	other	units	other	units	other	units
s	3086.20	m	3.09	km	1.93	mi	10184.46	ft
u	250.00	m/s	900.00	km/h	559.23	mi/h	820.21	ft/s
v	10.00	m/s	36.00	km/h	22.37	mi/h	32.81	ft/s
a	-8.00	m/s/s	avg.
t	30.00	s

	parachute deployment
	x	units	other	units	other	units	other	units
s	6.00	m	0.01	km	0.00	mi	19.80	ft
u	10.00	m/s	36.00	km/h	22.37	mi/h	32.81	ft/s
v	2.00	m/s	7.20	km/h	4.47	mi/h	6.56	ft/s
a	-8.00	m/s/s
t	1.00	s

	parachute floating
	x	units	other	units	other	units	other	units
s	239.00	m	0.24	km	0.15	mi	788.70	ft
u	2.00	m/s	7.20	km/h	4.47	mi/h	6.56	ft/s
v	0.00	m/s	0.00	km/h	0.00	mi/h	0.00	ft/s
a	-0.01	m/s/s
t	239.00	s


	net parachute
	x	units	other	units	other	units	other	units
s	1200.00	m	1.20	km	0.75	mi	3960.00	ft
u	10.00	m/s	36.00	km/h	22.37	mi/h	32.81	ft/s
v	0.00	m/s	0.00	km/h	0.00	mi/h	0.00	ft/s
a	-0.04	m/s/s	avg.
t	240.00	s

	net jump
	x	units	other	units	other	units	other	units
s	33750.00	m	33.75	km	21.09	mi	111375.00	ft
u	250.00	m/s	900.00	km/h	559.23	mi/h	820.21	ft/s
v	0.00	m/s	0.00	km/h	0.00	mi/h	0.00	ft/s
a	-0.93	m/s/s	avg.
t	270.00	s

	accelerated freefall
	y	units	other	units	other	units	other	units
s	-401.11	m	-0.40	km	-0.25	mi	-1323.67	ft
u	0.00	m/s	0.00	km/h	0.00	mi/h	0.00	ft/s
v	-52.78	m/s	-190.00	km/h	-118.06	mi/h	-173.16	ft/s
a	-3.47	m/s/s
t	15.20	s

	constant freefall
	y	units	other	units	other	units	other	units
s	-781.11	m	-0.78	km	-0.49	mi	-2577.67	ft
u	-52.78	m/s	-190.00	km/h	-118.06	mi/h	-173.16	ft/s
v	-52.78	m/s	-190.00	km/h	-118.06	mi/h	-173.16	ft/s
a	0.00	m/s/s
t	14.80	s

	net freefall
	y	units	other	units	other	units	other	units
s	-1182.22	m	-1.18	km	-0.74	mi	-3901.33	ft
u	0.00	m/s	0.00	km/h	0.00	mi/h	0.00	ft/s
v	-52.78	m/s	-190.00	km/h	-118.06	mi/h	-173.16	ft/s
a	-1.76	m/s/s	avg.
t	30.00	s


	parachutte deployment
	y	units	other	units	other	units	other	units
s	-29.17	m	-0.03	km	-0.02	mi	-96.25	ft
u	-52.78	m/s	-190.00	km/h	-118.06	mi/h	-173.16	ft/s
v	-5.56	m/s	-20.00	km/h	-12.43	mi/h	-18.23	ft/s
a	47.22	m/s/s	4.82	g's
t	1.00	s

	parachutte floating
	y	units	other	units	other	units	other	units
s	-1212.85	m	-1.24	km	-0.78	mi	-4098.67	ft
u	-5.56	m/s	-20.00	km/h	-12.43	mi/h	-18.23	ft/s
v	-5.56	m/s	-20.00	km/h	-12.43	mi/h	-18.23	ft/s
a	0.00	m/s/s
t	239.00	s

	net parachutte
	y	units	other	units	other	units	other	units
s	-1242.02	m	-1.24	km	-0.78	mi	-4098.67	ft
u	-52.78	m/s	-190.00	km/h	-118.06	mi/h	-173.16	ft/s
v	-5.56	m/s	-20.00	km/h	-12.43	mi/h	-18.23	ft/s
a	-0.20	m/s/s	avg.
t	240.00	s

	net jump
	y	units	other	units	other	units	other	units
s	-2424.24	m	-2.42	km	-1.52	mi	-8000.00	ft
u	0.00	m/s	0.00	km/h	0.00	mi/h	0.00	ft/s
v	-5.56	m/s	-20.00	km/h	-12.43	mi/h	-18.23	ft/s
a	0.02	m/s/s	avg.
t	270.00	s

This is a graph indicating Velocity over time. It does not include the entire jump, but just the first 38s because after that it continues in the same direction until the landing. The first 38s is the only place where there is major change. Down is +.

This is a graph of velocity over time for the same reason as velocity. Down is -. Data File

This is a graph of acceleration over time for the same reason as velocity. Data File

This is a x – y axis indicating the most likely path that would be followed by a skydiver when he/she jumps out of the plane. This graph does not take into account any wind that might affect the x axis at any time. It is almost impossible for us to measure the wind that might be present and how it affected the skydiver.

This is a graph of x vs y position. Data File

Discussion ▲

Our results ended up proving our hypothesis and the theories that they were based on. We found that a person does, once they jump out of the plane, in fact accelerate towards the ground at an initial acceleration of 9.8 m/s/s that instantaneously decreases as they continue on their jump. We also found that the terminal velocity of a person that is in the spread position is 190km/h which is reached after about 15s of accelerated freefall. After 30s into the jump, the skydiver pulls the cord to release the parachute. The parachute creates an upward acceleration of over 4 g’s, which is why the parachute can create such an almost instantaneous decrease in velocity. While descending with the parachute open, the skydiver has approximately 3 and a half minutes before landing. The problem with measuring the necessary data required to calculate the required formulas is that skydiving is expensive and you only get one chance, per jump, to measure what you are trying to find. Using the simulator, as well as the SUVAT and other formulas, we had sufficient data to recreate a complete skydive. If an accelerometer was used in the actual experiment, then there would have been less uncertainty that is created in using formulas. It is now possible to agree with the previous information given to us by our sources, concerning the physics of skydiving.

Method ▲

This is a graph of x vs y position. Data File

Discussion ▲

Back to top