## We get this questions a lot - so we wanted to clarify how we gather data and turn it into the metrics we output.

### 3D Position

Perch uses a 3D camera to directly measure the **position** of objects in the field of view of the camera. Every image that the Perch camera captures contains information about how far away objects are from the camera itself.

Using a complex tracking pipeline developed by engineers at Perch, the camera processes the image to find the objects we’re interested in (namely, a barbell, parts of the body, etc). Once the object is located in the image, the device will use the distance data from the 3D camera and some geometry to triangulate where the object is in 3D space. Otherwise known as determining the **3D coordinate of the object for this particular point in time.**

3D position, as its name suggests, consists of three spatial dimensions. The names we use for these dimensions are X, Y, and Z. We define Z as **up and down (parallel to gravity)**, X as **forwards and backwards (in the perspective of the athlete)**, and Y as **side to side (in the perspective of the athlete)**.

### 3D Path

The 3D path of an object -- in our case, usally a barbell -- is nothing more than a sequence of 3D coordinates with time stamps. By processing images rapidly as the 3D camera captures them, we collect many 3D coordinates and collect them together to form a 3D path.

The 3D path represents precisely **where in 3D space an object moved over time**. This is the core data that Perch captures, and every other metric is calculated using this 3D path.

### Displacement

Displacement is simply calculated by **subtracting a starting 3D position and from an ending position**. If you isolate only one of the axes, for example the Z axis, you then have the **vertical displacement** between those positions. For example, in the case of a back squat, the displacement on the Z axis can be interpreted as the **squat depth**.

### Velocity

The equation for velocity is always the same: **displacement (aka. distance) divided by time**. Since we are able to go from 3D position to 3D Path and finally calculate displacement, we’re halfway there. Every 3D coordinate also has a corresponding time associated with it, and we can subtract the times starting and ending 3D coordinates to calculate the **amount of time elapsed between those two positions.**

By dividing the displacement by the time that elapsed between them, you are calculating velocity.

### Mean Velocity

Mean velocity (or average velocity) as used in VBT is defined as the average velocity of a complete movement (e.g. the concentric portion of a rep).

Calculating mean velocity is exactly the same as calculating any other velocity, except the **start and end 3D positions you choose are the beginning and end of the movement respectively**.

For example, to calculate the concentric mean velocity (on the Z axis) of a rep, we perform three calculations:

- We subtract the Z value of the coordinate of the bottom of the rep (the beginning of the concentric movement) from the highest point at the end of the rep (the final coordinate of the concentric movement) to calculate the displacement.
- We subtract the times of the same two coordinates chosen above to calculate the duration of the concentric movement
- Finally, we divide the displacement by the duration to get the velocity

Concentric and Eccentric Mean Velocity are both captured in the system and are registered separately - one will not impact the other.

### Peak Velocity

Calculating peak velocity is once again very similar to other velocity calculations, however it differs in selection of the coordinates.

Peak velocity is defined as the **greatest instantaneous velocity during a movement**. Here, “instantaneous” means **between two consecutive coordinates**. Naturally, there is some amount of time between each coordinate we measure, so using two adjacent coordinates is not *truly* instantaneous, but is sufficiently close.

As an example, to find the peak concentric velocity (on the Z axis), we do the following:

- Compute the instantaneous velocity using every pair of consecutive coordinates from the lowest to the highest point of the movement (following the same procedure as defined above)
- The largest of these instantaneous velocities is your peak concentric velocity

### Eccentric Time

Eccentric time is tracking the amount of time, in seconds, it takes to complete the eccentric portion of the movement. This is not displayed on the tablet for Olympic lifts or for jumps.

We subtract the Z value of the coordinate of the top of the rep (the beginning of the eccentric movement) from the lowest point at the end of the rep (the final coordinate of the eccentric movement). We subtract the times of the same two coordinates to calculate the duration of the eccentric movement.### Power

The equation for power is defined as **Work divided by time**: **P = W / t**

With some algebra and substitution using other physics equations, the equation for power can be rewritten in a few helpful ways**:**

**W = F d F = m a V = ****d / ****t**

**P = ****F d / ****t**

**P = F V P = m a V**

In our case, the force is how much force the athlete is applying to the babell. While we’ve already covered how we can calculate velocity (the Vterm), we can’t directly measure the force. However, we can calculate it in a couple different ways depending on the context.

### Mean Power

Mean power can be described as the **average amount of power over the duration of the movement**. To calculate, we can reuse the *mean velocity* we’ve already calculated above for the V term in our power equations.

The force (F) in our equation is similarly the **average force applied by the athlete during the movement**. Because the bar is at rest before and after the movement, the average force is equal to the force required to oppose gravity (aka, the force of gravity) on the barbell. As such, the force is **the mass of the barbell (in kilograms) multiplied by the acceleration due to gravity (9.8 m/s)**.

With the math established, calculating mean power is as simple as substituting the mass of the barbell (converted to kilograms, m) and the mean velocity (in meters per second, V) into the following equation:

**Mean Power** = **m **x **9.8 **x **V**

### Peak Power

Calculating peak power requires a bit more complexity, as was the case with *peak velocity*.

In order to calculate the peak power output for a movement, we calculate **the instantaneous power at every point during the movement, and select the largest**.

Here is the general procedure for how we calculate peak power for a concentric movement:

- Using the same procedure as in
*peak velocity*, calculate the instantaneous velocity for every pair of points in the movement - Using every consecutive pair of instantaneous velocities computed in 1, compute the instantaneous acceleration (acceleration is
**change in velocity divided by time**) - For each instantaneous measurement of velocity and acceleration, plug in the following variables
- The instantaneous acceleration (a)
- The instantaneous velocity (V)
- The weight in kilograms of the barbell (m)

**Peak Power = m **x** a **x **V**

- Select the largest value, this is your peak power

### Work

As we referenced in the sections discussing Power, Work can be calculated as W = Fd where F is the average force applied by the athlete to the barbell and d is the displacement of the movement. Work is presented in units of Kilojoules (kJ), which is a measure of Energy. Work can be thought of as the amount of energy the athlete put into the barbell by lifting it against gravity.

### Time to Peak Power (T2PP)

Based on the calculation for Peak Power above (Peak Power = m x a x V), the time to peak power is the duration in seconds it takes to achieve that peak power, based on the start of the concentric portion of the rep. This is displayed as T2PP as an abbreviation in the app.

### Time to Peak Velocity (T2PV)

Based on the calculation for Peak Velocity above, the time to peak velocity is the duration in seconds it takes to achieve that peak velocity, based on the start of the concentric portion of the rep. This is displayed as T2PV as an abbreviation in the app.

### Velocity at 100ms (V100)

The v100 is a new metric that will help to track explosiveness of athletes, among other things. This is based similarly to calculations above of time to peak velocity and power, but instead measures the velocity at which the bar is moving within the first 100 milliseconds of the concentric portion of the rep. This is displayed as V100 as an abbreviation in the app.

### Jump Assessment Concepts

Jump assessments have special metrics calculated specifically for them. These metrics are built off of the same tracking technology used for other exercises. Here's what you need to know.

### Types of Jumping

#### Counter Movement Jump (CMJ)

A counter movement jump is defined in Perch as a jump where the athlete begins by standing up straight, dips into a preload by bending knees and hips to a self-selected depth, and then rapidly explodes out of their preload into a vertical jump as high as possible.

When performing multiple repetitions, the athlete should land from their previous jump, reset, and return to their original standing position before beginning their next jump.

#### Continuous Jumps

A continuous jumping exercise starts similarly to a counter movement jump. The athlete will stand up straight before preloading to a self-selected depth, and then explode into their first repetition of a vertical jump.

**However**, instead of landing and pausing to return to a standing position, the athlete’s landing from the previous jump flows smoothly into the preload of their next jump. Thus, the athlete performs multiple jumps without rest in between. A priority should be minimizing ground contact time while maximizing jump height.

#### Tracking a Jump

Because Perch measures 3D position of objects, we track the position of parts of the athlete’s body to track jumps and other non-barbell exercises. The primary object used for tracking jumps is the athlete’s head.

To track a jump, Perch uses the position of the athlete's head right before beginning their jump to measure their standing height. When the athlete begins unweighting, for either a CMJ or Continuous Jumps, that marks the **beginning of the jump**.

For continuous jumps, the **beginning** of each repetition after the athlete’s first is the same as the **moment the athlete lands** from the previous repetition.

After preloading, the athlete explodes upwards into their jump (the propulsive phase). The moment the athlete returns to their original starting height (the end of the propulsive phase) is defined as the** moment of takeoff**. The athlete’s feet will leave the ground at this moment in time.

During the jump, the athlete rises and falls in the air (the flight phase). The **apex of the jump **can be measured as the highest point the athlete reaches after takeoff. The **moment the athlete lands** is the moment when the athlete falls back to their original standing height, before decelerating and absorbing the landing.

### Jump Height

Jump height is a measure of displacement. Given the above definitions, Perch measures jump height simply by subtracting the height of the **apex of the jump **from the athlete’s standing height before the** beginning of the jump**.

### Time To Takeoff

Time to takeoff is measured as the amount of time elapsed between the **beginning of the jump** (the start of the unweighting phase) until the **moment of takeoff** (the end of the propulsive phase).

This time includes the full duration of the following jump phases:

- Unweighting
- Braking
- Propulsive

### Takeoff Velocity

Takeoff velocity is a measure of instantaneous velocity at the **moment of takeoff** (the end of the propulsive phase). This is the speed at which the athlete is moving just before their feet leave the ground after the propulsive phase.

### RSIMod

RSIMod is Jump Height divided by Time to Takeoff. It is reported as a unitless quantity, rather than its true unit of m/s, since it should not be interpreted as a velocity.