R/samozino.R
In mladenjovanovic/vjsim: Vertical Jump Simulator
Defines functions
make_samozino_profile
get_samozino_profile
probe_samozino_take_off_velocity
get_samozino_jump_metrics
get_all_samozino_profiles
get_samozino_optimal_profile
get_samozino_take_off_velocity
Documented in
get_all_samozino_profiles
get_samozino_jump_metrics
get_samozino_optimal_profile
get_samozino_profile
get_samozino_take_off_velocity
make_samozino_profile
probe_samozino_take_off_velocity
#' Get Samozino Take-Off Velocity
#'
#' \code{get_samozino_take_off_velocity} returns predicted maximal take off velocity that could be achieve based on the Samozino \emph{et al.}
#' model which uses vertical jump profile \code{F0} and \code{V0}.
#' @param F0 Numeric vector. Default 3000
#' @param V0 Numeric vector. Default 4
#' @param bodyweight Numeric vector. Default 75
#' @param push_off_distance Numeric vector. Default 0.4
#' @param gravity_const Numeric vector. Default 9.81
#' @return Numeric vector representing maximal take-off velocity
#' @export
#' @references
#' Samozino, Pierre. ‘A Simple Method for Measuring Lower Limb Force, Velocity and Power Capabilities During Jumping’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 65–96. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_4.
#'
#' ———. ‘Optimal Force-Velocity Profile in Ballistic Push-off: Measurement and Relationship with Performance’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 97–119. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_5.
#'
#' Samozino, Pierre, Jean-Benoît Morin, Frédérique Hintzy, and Alain Belli. ‘Jumping Ability: A Theoretical Integrative Approach’. Journal of Theoretical Biology 264, no. 1 (May 2010): 11–18. https://doi.org/10.1016/j.jtbi.2010.01.021.
#'
#' Samozino, Pierre, Enrico Rejc, Pietro Enrico Di Prampero, Alain Belli, and Jean-Benoît Morin. ‘Optimal Force–Velocity Profile in Ballistic Movements—Altius’: Medicine & Science in Sports & Exercise 44, no. 2 (February 2012): 313–22. https://doi.org/10.1249/MSS.0b013e31822d757a.
#' @examples
#' get_samozino_take_off_velocity(F0 = 2500, V0 = 3.7, bodyweight = 85, push_off_distance = 0.42)
get_samozino_take_off_velocity <- function(F0 = 3000,
V0 = 4,
bodyweight = 75,
push_off_distance = 0.4,
gravity_const = 9.81) {
(push_off_distance * (sqrt(F0^2 / (4 * V0^2) - (2 * bodyweight * (gravity_const * bodyweight - F0)) / push_off_distance) - F0 / (2 * V0))) / bodyweight
}
#' Get Samozino's Optimal Profile
#'
#' \code{get_samozino_optimal_profile} finds optimal Force-Velocity profile that maximizes vertical jump height based on the model of
#' Samozino \emph{et al.}. According to this model, we are looking for Force-Velocity profile that maintains the max power, but changes
#' \code{F0} and \code{V0} so it maximized the take-off velocity calculated using \code{\link{get_samozino_take_off_velocity}}.
#' @param F0 Numeric value. Default 3000
#' @param V0 Numeric value. Default 4
#' @param bodyweight Numeric value. Default 75
#' @param push_off_distance Numeric value. Default 0.4
#' @param gravity_const Numeric value. Default 9.81
#' @return List
#' @export
#' @references
#' Samozino, Pierre. ‘A Simple Method for Measuring Lower Limb Force, Velocity and Power Capabilities During Jumping’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 65–96. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_4.
#'
#' ———. ‘Optimal Force-Velocity Profile in Ballistic Push-off: Measurement and Relationship with Performance’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 97–119. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_5.
#'
#' Samozino, Pierre, Jean-Benoît Morin, Frédérique Hintzy, and Alain Belli. ‘Jumping Ability: A Theoretical Integrative Approach’. Journal of Theoretical Biology 264, no. 1 (May 2010): 11–18. https://doi.org/10.1016/j.jtbi.2010.01.021.
#'
#' Samozino, Pierre, Enrico Rejc, Pietro Enrico Di Prampero, Alain Belli, and Jean-Benoît Morin. ‘Optimal Force–Velocity Profile in Ballistic Movements—Altius’: Medicine & Science in Sports & Exercise 44, no. 2 (February 2012): 313–22. https://doi.org/10.1249/MSS.0b013e31822d757a.
#' @examples
#' get_samozino_optimal_profile(F0 = 2500, V0 = 3.7, bodyweight = 85, push_off_distance = 0.42)
get_samozino_optimal_profile <- function(F0 = 3000,
V0 = 4,
bodyweight = 75,
push_off_distance = 0.4,
gravity_const = 9.81) {
# Dataframe to be forwarded to optim function
data <- data.frame(
F0 = F0,
V0 = V0,
bodyweight = bodyweight,
push_off_distance = push_off_distance,
gravity_constant = gravity_const
)
take_off_velocity <- get_samozino_take_off_velocity(F0, V0, bodyweight, push_off_distance, gravity_const)
# Probe TOV
take_off_velocity_v_increase <- get_samozino_take_off_velocity(F0, V0 * 1.1, bodyweight, push_off_distance, gravity_const)
take_off_velocity_f_increase <- get_samozino_take_off_velocity(F0 * 1.1, V0, bodyweight, push_off_distance, gravity_const)
# function to be returned to optim
opt_jump_func <- function(par, data) {
new_F0 <- data$F0 / par[1]
new_V0 <- data$V0 * par[1]
take_off_velocity <- get_samozino_take_off_velocity(
new_F0,
new_V0,
data$bodyweight,
data$push_off_distance,
data$gravity_const
)
return(1 / take_off_velocity)
}
# ------------------------
# Find optimal parameters
upper_bound <- (F0 / bodyweight) / gravity_const
get_optim_model <- function() {
tryCatch(
{
stats::optim(par = 1, fn = opt_jump_func, data = data, method = "Brent", lower = 0, upper = upper_bound)
},
error = function(cond) {
return(list(par = NA, value = NA))
},
warning = function(cond) {
return(list(par = NA, value = NA))
}
)
}
results <- get_optim_model()
# Save the results
Sfv <- get_slope(F0, V0)
Sfv_rel <- Sfv / bodyweight
optimal_F0 <- F0 / results$par[1]
optimal_V0 <- V0 * results$par[1]
optimal_Sfv <- get_slope(optimal_F0, optimal_V0)
optimal_Sfv_rel <- optimal_Sfv / bodyweight
optimal_take_off_velocity <- 1 / results$value
optimal_height <- get_height(optimal_take_off_velocity, gravity_const)
optimal_Pmax <- get_max_power(optimal_F0, optimal_V0)
height <- get_height(take_off_velocity, gravity_const)
df <- list(
F0 = F0,
F0_rel = F0 / bodyweight,
V0 = V0,
Pmax = get_max_power(F0, V0),
Pmax_rel = get_max_power(F0, V0) / bodyweight,
Sfv = Sfv,
Sfv_rel = Sfv_rel,
take_off_velocity = take_off_velocity,
height = height,
optimal_F0 = optimal_F0,
optimal_F0_rel = optimal_F0 / bodyweight,
optimal_V0 = optimal_V0,
optimal_height = optimal_height,
optimal_height_diff = optimal_height - height,
optimal_height_ratio = optimal_height / height,
optimal_Pmax = optimal_Pmax,
optimal_Pmax_rel = optimal_Pmax / bodyweight,
optimal_take_off_velocity = optimal_take_off_velocity,
optimal_take_off_velocity_diff = optimal_take_off_velocity - take_off_velocity,
optimal_take_off_velocity_ratio = optimal_take_off_velocity / take_off_velocity,
optimal_Sfv = optimal_Sfv,
optimal_Sfv_rel = optimal_Sfv_rel,
Sfv_perc = (Sfv / optimal_Sfv) * 100,
FV_imbalance = abs(1 - (Sfv / optimal_Sfv)) * 100,
probe_IMB = (take_off_velocity_v_increase - take_off_velocity) / (take_off_velocity_f_increase - take_off_velocity) * 100
)
return(df)
}
#' Get All Samozino profiles
#'
#' \code{get_all_samozino_profiles} returns theoretical and practical Samozino profiles using \code{profile_data}
#' returned from the \code{\link{vj_profile}} and \code{\link{get_samozino_optimal_profile}} functions
#' @param profile_data Data frame returned from \code{\link{vj_profile}} function
#' @return List with two elements: list of profiles and long data frame
#' @export
#' @references
#' Samozino, Pierre. ‘A Simple Method for Measuring Lower Limb Force, Velocity and Power Capabilities During Jumping’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 65–96. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_4.
#'
#' ———. ‘Optimal Force-Velocity Profile in Ballistic Push-off: Measurement and Relationship with Performance’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 97–119. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_5.
#'
#' Samozino, Pierre, Jean-Benoît Morin, Frédérique Hintzy, and Alain Belli. ‘Jumping Ability: A Theoretical Integrative Approach’. Journal of Theoretical Biology 264, no. 1 (May 2010): 11–18. https://doi.org/10.1016/j.jtbi.2010.01.021.
#'
#' Samozino, Pierre, Enrico Rejc, Pietro Enrico Di Prampero, Alain Belli, and Jean-Benoît Morin. ‘Optimal Force–Velocity Profile in Ballistic Movements—Altius’: Medicine & Science in Sports & Exercise 44, no. 2 (February 2012): 313–22. https://doi.org/10.1249/MSS.0b013e31822d757a.
#' @examples
#' fv_profile <- vj_profile(mass = 75)
#' all_samozino_profiles <- get_all_samozino_profiles(fv_profile)
#' all_samozino_profiles$data_frame
get_all_samozino_profiles <- function(profile_data) {
# Theoretical Samozino profile
# Uses mean velocity of the profile
jump_profile <- get_FV_profile(
profile_data,
force = "mean_GRF_over_distance",
velocity = "mean_velocity"
)
samozino_theoretical_profile <- get_samozino_optimal_profile(
F0 = jump_profile$F0,
V0 = jump_profile$V0,
bodyweight = profile_data$bodyweight[1],
push_off_distance = profile_data$push_off_distance[1],
gravity_const = profile_data$gravity_const[1]
)
# Practical Samozino profile
# Uses half of take-off velocity as mean velocity
# This is easier to measure without laboratory conditions
jump_profile <- get_FV_profile(
profile_data,
force = "mean_GRF_over_distance",
velocity = "mean_velocity_as_TOV_half"
)
samozino_practical_profile <- get_samozino_optimal_profile(
F0 = jump_profile$F0,
V0 = jump_profile$V0,
bodyweight = profile_data$bodyweight[1],
push_off_distance = profile_data$push_off_distance[1],
gravity_const = profile_data$gravity_const[1]
)
# Bind them together
profiles_list <- list(
samozino_theoretical_profile = samozino_theoretical_profile,
samozino_practical_profile = samozino_practical_profile
)
profiles_df <- dplyr::bind_rows(profiles_list, .id = "profile")
profiles_df <- tidyr::gather(profiles_df, "metric", "value", -1, na.rm = TRUE)
profiles_df$profile <- factor(
profiles_df$profile,
levels = c(
"samozino_practical_profile",
"samozino_theoretical_profile"
),
labels = c(
"Samozino practical profile",
"Samozino theoretical profile"
)
)
# Sort data frame
profiles_df <- profiles_df[order(profiles_df$profile), ]
return(list(
list = profiles_list,
data_frame = profiles_df
))
}
#' Get Samozino Jump Metrics
#'
#' \code{get_samozino_jump_metrics} return mean force, mean velocity and mean power using simple method explained in
#' the references.
#' @param mass Numeric vector. Default 75
#' @param push_off_distance Numeric vector. Default 0.4
#' @param height Numeric vector. Jump height. Default 0.5
#' @param gravity_const Numeric vector. Default 9.81
#' @return List with \code{mass}, \code{push_off_distance}, \code{height}, \code{gravity_const}, \code{mean_GRF_over_distance},
#' \code{mean_velocity}, \code{take_off_velocity}, and \code{mean_power}
#' @references
#' Samozino, Pierre. ‘A Simple Method for Measuring Lower Limb Force, Velocity and Power Capabilities During Jumping’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 65–96. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_4.
#'
#' ———. ‘Optimal Force-Velocity Profile in Ballistic Push-off: Measurement and Relationship with Performance’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 97–119. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_5.
#'
#' Samozino, Pierre, Jean-Benoît Morin, Frédérique Hintzy, and Alain Belli. ‘Jumping Ability: A Theoretical Integrative Approach’. Journal of Theoretical Biology 264, no. 1 (May 2010): 11–18. https://doi.org/10.1016/j.jtbi.2010.01.021.
#'
#' Samozino, Pierre, Enrico Rejc, Pietro Enrico Di Prampero, Alain Belli, and Jean-Benoît Morin. ‘Optimal Force–Velocity Profile in Ballistic Movements—Altius’: Medicine & Science in Sports & Exercise 44, no. 2 (February 2012): 313–22. https://doi.org/10.1249/MSS.0b013e31822d757a.
#' @export
#' @examples
#' get_samozino_jump_metrics(
#' mass = 75,
#' push_off_distance = 0.43,
#' height = 0.45
#' )
get_samozino_jump_metrics <- function(mass = 75,
push_off_distance = 0.4,
height = 0.5,
gravity_const = 9.81) {
mean_GRF_over_distance <- mass * gravity_const * (height / push_off_distance + 1)
mean_velocity <- sqrt(gravity_const * height / 2)
mean_power <- mean_GRF_over_distance * mean_velocity
return(list(
mass = mass,
push_off_distance = push_off_distance,
height = height,
gravity_const = gravity_const,
mean_GRF_over_distance = mean_GRF_over_distance,
mean_velocity = mean_velocity,
# this is equal to sqrt(2 * gravity_const * height),
take_off_velocity = mean_velocity * 2,
mean_power = mean_power
))
}
#' Probe Samozino Take-off Velocity
#'
#' \code{probe_samozino_take_off_velocity} probes results of the \code{\link{get_samozino_take_off_velocity}} function by varying
#' \code{F0}, \code{V0}, and \code{bodyweight} parameters
#' @param F0 Numeric vector. Default 3000
#' @param V0 Numeric vector. Default 4
#' @param bodyweight Numeric vector. Default 75
#' @param push_off_distance Numeric vector. Default 0.4
#' @param gravity_const Numeric vector. Default 9.81
#' @param change_ratio Numeric vector indicating probing change ratios
#' @param aggregate How should \code{\link{get_samozino_take_off_velocity}} output be aggregated?
#' Default is "raw". Other options involve "ratio" and "diff" which use initial
#' output values
#' @return Probing data frame
#' @export
#' @examples
#' require(ggplot2)
#'
#' samozino_probe_data <- probe_samozino_take_off_velocity(
#' F0 = 3000,
#' V0 = 3.5,
#' push_off_distance = 0.4,
#' bodyweight = 75,
#' change_ratio = seq(0.8, 1.2, length.out = 1001)
#' )
#'
#' ggplot(
#' samozino_probe_data,
#' aes(
#' x = change_ratio,
#' y = take_off_velocity,
#' color = probing
#' )
#' ) +
#' geom_line()
probe_samozino_take_off_velocity <- function(F0 = 3000,
V0 = 4,
bodyweight = 75,
push_off_distance = 0.4,
gravity_const = 9.81,
change_ratio = seq(0.9, 1.1, length.out = 3),
aggregate = "raw") {
get_probing_data(
args_list = list(F0 = F0, V0 = V0, bodyweight = bodyweight),
probe_func = function(...) list(take_off_velocity = get_samozino_take_off_velocity(...)),
change_ratio = change_ratio,
aggregate = aggregate,
push_off_distance = push_off_distance,
gravity_const = gravity_const
)
}
#' Get Samozino Profile
#'
#' \code{get_samozino_profile} returns Samozino model estimated from known \code{bodyweight}, \code{push_off_distance},
#' \code{mean_GRF_over_distance}, \code{mean_velocity} and \code{gravity_const}.
#' @param bodyweight Numeric value
#' @param push_off_distance Numeric value
#' @param mean_GRF_over_distance Numeric vector
#' @param mean_velocity Numeric vector
#' @param gravity_const Numeric value
#' @return Object returned from \code{\link{get_samozino_optimal_profile}} with addition of RSE and R_Squared elements
#' @references
#' Samozino, Pierre. ‘A Simple Method for Measuring Lower Limb Force, Velocity and Power Capabilities During Jumping’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 65–96. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_4.
#'
#' ———. ‘Optimal Force-Velocity Profile in Ballistic Push-off: Measurement and Relationship with Performance’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 97–119. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_5.
#'
#' Samozino, Pierre, Jean-Benoît Morin, Frédérique Hintzy, and Alain Belli. ‘Jumping Ability: A Theoretical Integrative Approach’. Journal of Theoretical Biology 264, no. 1 (May 2010): 11–18. https://doi.org/10.1016/j.jtbi.2010.01.021.
#'
#' Samozino, Pierre, Enrico Rejc, Pietro Enrico Di Prampero, Alain Belli, and Jean-Benoît Morin. ‘Optimal Force–Velocity Profile in Ballistic Movements—Altius’: Medicine & Science in Sports & Exercise 44, no. 2 (February 2012): 313–22. https://doi.org/10.1249/MSS.0b013e31822d757a.
#' @export
#' @examples
#' require(tidyverse)
#' data("testing_data")
#'
#' testing_data <- testing_data %>%
#' mutate(
#' height = vjsim::get_height_from_aerial_time(aerial_time),
#' total_load = bodyweight + external_load
#' )
#'
#' jump_metric <- function(data) {
#' samozino_metrics <- vjsim::get_samozino_jump_metrics(
#' mass = data$bodyweight + data$external_load,
#' push_off_distance = data$push_off_distance,
#' height = data$height
#' )
#' return(as.data.frame(samozino_metrics))
#' }
#'
#'
#' testing_data <- testing_data %>%
#' # Need to add bodyweight so it is kept in the output
#' group_by(athlete, bodyweight) %>%
#' do(jump_metric(.))
#'
#' samozino_profile <- function(data) {
#' samozino_data <- vjsim::get_samozino_profile(
#' bodyweight = data$bodyweight,
#' push_off_distance = data$push_off_distance,
#' mean_GRF_over_distance = data$mean_GRF_over_distance,
#' mean_velocity = data$mean_velocity
#' )
#'
#' return(as.data.frame(samozino_data))
#' }
#'
#' testing_data_samozino <- testing_data %>%
#' # Need to add bodyweight so it is kept in the output
#' group_by(athlete, bodyweight) %>%
#' do(samozino_profile(.))
#'
#' testing_data_samozino
get_samozino_profile <- function(bodyweight,
push_off_distance,
mean_GRF_over_distance,
mean_velocity,
gravity_const = 9.81) {
# Check if any of the parameters is NA and return a list with NA
if (any(
is.na(bodyweight),
is.na(push_off_distance),
is.na(mean_GRF_over_distance),
is.na(mean_velocity),
is.na(gravity_const)
)) {
return(lapply(
get_samozino_optimal_profile(
F0 = 5000,
V0 = 4,
bodyweight = 100,
push_off_distance = 0.4,
gravity_const = 10
),
function(x) {
NA
}
))
}
profile_data <- data.frame(
bodyweight = bodyweight,
mean_GRF_over_distance = mean_GRF_over_distance,
mean_velocity = mean_velocity
)
jump_profile <- get_FV_profile(
profile_data,
force = "mean_GRF_over_distance",
velocity = "mean_velocity"
)
# Calculate residual standard error and R^2
predicted_mean_velocity <- jump_profile$V0 + mean_GRF_over_distance / jump_profile$Sfv
RSE <- sqrt(sum((predicted_mean_velocity - mean_velocity)^2) / (length(mean_velocity) - 2))
R_squared <- stats::cor(predicted_mean_velocity, mean_velocity)^2
samozino_profile <- get_samozino_optimal_profile(
F0 = jump_profile$F0,
V0 = jump_profile$V0,
bodyweight = bodyweight[1],
push_off_distance = push_off_distance[1],
gravity_const = gravity_const[1]
)
samozino_profile$RSE <- RSE
samozino_profile$R_squared <- R_squared
return(samozino_profile)
}
#' Make Samozino Profile
#'
#' \code{make_samozino_profile} generates Samozino profile from squat jump data. When both \code{aerial_time} and
#' \code{height} are forwarded to the function, only \code{height} is used to estimate mean GRF.
#'
#' @param bodyweight Numeric value
#' @param push_off_distance Numeric value
#' @param external_load Numeric vector
#' @param height Numeric vector
#' @param aerial_time Numeric vector
#' @param gravity_const Numeric vector. Default 9.81
#' @param plot TRUE/FALSE. Default is TRUE
#' @return List of Samozino profile parameters
#' @export
#' @references
#' Samozino, Pierre. ‘A Simple Method for Measuring Lower Limb Force, Velocity and Power Capabilities During Jumping’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 65–96. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_4.
#'
#' ———. ‘Optimal Force-Velocity Profile in Ballistic Push-off: Measurement and Relationship with Performance’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 97–119. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_5.
#'
#' Samozino, Pierre, Jean-Benoît Morin, Frédérique Hintzy, and Alain Belli. ‘Jumping Ability: A Theoretical Integrative Approach’. Journal of Theoretical Biology 264, no. 1 (May 2010): 11–18. https://doi.org/10.1016/j.jtbi.2010.01.021.
#'
#' Samozino, Pierre, Enrico Rejc, Pietro Enrico Di Prampero, Alain Belli, and Jean-Benoît Morin. ‘Optimal Force–Velocity Profile in Ballistic Movements—Altius’: Medicine & Science in Sports & Exercise 44, no. 2 (February 2012): 313–22. https://doi.org/10.1249/MSS.0b013e31822d757a.
#' @examples
#' require(tidyverse)
#'
#' data("testing_data")
#'
#' with(
#' filter(testing_data, athlete == "Jack"),
#' make_samozino_profile(
#' bodyweight = bodyweight,
#' push_off_distance = push_off_distance,
#' external_load = external_load,
#' aerial_time = aerial_time,
#' plot = TRUE
#' )
#' )
make_samozino_profile <- function(bodyweight,
push_off_distance,
external_load,
height,
aerial_time,
gravity_const = 9.81,
plot = TRUE) {
# Check if both height and aerial_time are used
if (!missing(height) & !missing(aerial_time)) {
warning("Please use either height or aerial time as a parameter. Using height to model", call. = FALSE)
}
# If height missing, use aerial time to create it
if (missing(height)) {
height <- get_height_from_aerial_time(aerial_time, gravity_const)
}
# Get Force-Velocity profile
samozino_metrics <- get_samozino_jump_metrics(
mass = bodyweight + external_load,
push_off_distance = push_off_distance,
height = height,
gravity_const = gravity_const
)
# Get Samozino optimal profile
samozino_model <- get_samozino_profile(
bodyweight = bodyweight,
push_off_distance = push_off_distance,
mean_GRF_over_distance = samozino_metrics$mean_GRF_over_distance,
mean_velocity = samozino_metrics$mean_velocity,
gravity_const = gravity_const
)
# Create plot
if (plot) {
# Define function to calculate TOV from mean force
get_tov <- function(mass, gravity_const, mean_force, push_off_distance) {
sqrt((2 * push_off_distance * (mean_force - mass * gravity_const)) / mass)
}
plot_data <- data.frame(
group = rep(1:2, each = 2),
x = c(samozino_model$F0, 0),
y = c(0, samozino_model$V0)
)
plot_data_optimal <- data.frame(
group = rep(1:2, each = 2),
x = c(samozino_model$optimal_F0, 0),
y = c(0, samozino_model$optimal_V0)
)
mean_force_df <- expand.grid(
mass = bodyweight,
gravity_const = gravity_const,
push_off_distance = push_off_distance,
mean_GRF_over_distance = seq(min(bodyweight) * gravity_const, max(samozino_model$F0, samozino_model$optimal_F0))
)
mean_force_df$MV <- get_tov(
mass = bodyweight,
gravity_const = gravity_const,
mean_force = mean_force_df$mean_GRF_over_distance,
push_off_distance = push_off_distance
) / 2
gg <- ggplot2::ggplot() +
cowplot::theme_cowplot(8) +
ggplot2::geom_line(
ggplot2::aes(
x = mean_force_df$mean_GRF_over_distance,
y = mean_force_df$MV
),
alpha = 0.8,
color = "grey"
) +
ggplot2::geom_point(
ggplot2::aes(
x = samozino_metrics$mean_GRF_over_distance,
y = samozino_metrics$mean_velocity
),
alpha = 0.8
) +
ggplot2::geom_line(
ggplot2::aes(
x = plot_data$x,
y = plot_data$y
),
alpha = 0.8
) +
ggplot2::geom_line(
ggplot2::aes(
x = plot_data_optimal$x,
y = plot_data_optimal$y
),
alpha = 0.8,
linetype = "dashed"
) +
ggplot2::xlab("Mean GRF [N]") +
ggplot2::ylab("Mean Velocity [m/s]") +
ggplot2::ggtitle(
"Samozino profile",
paste(
"F0 = ", round(samozino_model$F0, 0), "N",
"; V0 = ", round(samozino_model$V0, 2), "m/s",
"; Pmax = ", round(samozino_model$Pmax, 0), "W",
"; Sfv = ", round(samozino_model$Sfv, 0),
"; Height = ", round(samozino_model$height, 2), "m",
"; RSE = ", round(samozino_model$RSE, 2), "m/s",
"; R2 = ", round(samozino_model$R_squared, 2),
"\n",
"Optimal: ",
"F0 = ", round(samozino_model$optimal_F0, 0), "N",
"; V0 = ", round(samozino_model$optimal_V0, 2), "m/s",
"; Pmax = ", round(samozino_model$optimal_Pmax, 0), "W",
"; Sfv = ", round(samozino_model$optimal_Sfv, 0),
"; Height = ", round(samozino_model$optimal_height, 2), "m",
"\n",
"Sfv% = ", round(samozino_model$Sfv_perc, 2),
"; FVimb = ", round(samozino_model$FV_imbalance, 2),
sep = ""
)
)
plot(gg)
}
return(samozino_model)
}
mladenjovanovic/vjsim documentation built on Aug. 7, 2020, 10:10 p.m.
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Defines functions make_samozino_profile get_samozino_profile probe_samozino_take_off_velocity get_samozino_jump_metrics get_all_samozino_profiles get_samozino_optimal_profile get_samozino_take_off_velocity
Documented in get_all_samozino_profiles get_samozino_jump_metrics get_samozino_optimal_profile get_samozino_profile get_samozino_take_off_velocity make_samozino_profile probe_samozino_take_off_velocity
#' Get Samozino Take-Off Velocity
#'
#' \code{get_samozino_take_off_velocity} returns predicted maximal take off velocity that could be achieve based on the Samozino \emph{et al.}
#' model which uses vertical jump profile \code{F0} and \code{V0}.
#' @param F0 Numeric vector. Default 3000
#' @param V0 Numeric vector. Default 4
#' @param bodyweight Numeric vector. Default 75
#' @param push_off_distance Numeric vector. Default 0.4
#' @param gravity_const Numeric vector. Default 9.81
#' @return Numeric vector representing maximal take-off velocity
#' @export
#' @references
#' Samozino, Pierre. ‘A Simple Method for Measuring Lower Limb Force, Velocity and Power Capabilities During Jumping’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 65–96. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_4.
#'
#' ———. ‘Optimal Force-Velocity Profile in Ballistic Push-off: Measurement and Relationship with Performance’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 97–119. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_5.
#'
#' Samozino, Pierre, Jean-Benoît Morin, Frédérique Hintzy, and Alain Belli. ‘Jumping Ability: A Theoretical Integrative Approach’. Journal of Theoretical Biology 264, no. 1 (May 2010): 11–18. https://doi.org/10.1016/j.jtbi.2010.01.021.
#'
#' Samozino, Pierre, Enrico Rejc, Pietro Enrico Di Prampero, Alain Belli, and Jean-Benoît Morin. ‘Optimal Force–Velocity Profile in Ballistic Movements—Altius’: Medicine & Science in Sports & Exercise 44, no. 2 (February 2012): 313–22. https://doi.org/10.1249/MSS.0b013e31822d757a.
#' @examples
#' get_samozino_take_off_velocity(F0 = 2500, V0 = 3.7, bodyweight = 85, push_off_distance = 0.42)
get_samozino_take_off_velocity <- function(F0 = 3000,
V0 = 4,
bodyweight = 75,
push_off_distance = 0.4,
gravity_const = 9.81) {
(push_off_distance * (sqrt(F0^2 / (4 * V0^2) - (2 * bodyweight * (gravity_const * bodyweight - F0)) / push_off_distance) - F0 / (2 * V0))) / bodyweight
}
#' Get Samozino's Optimal Profile
#'
#' \code{get_samozino_optimal_profile} finds optimal Force-Velocity profile that maximizes vertical jump height based on the model of
#' Samozino \emph{et al.}. According to this model, we are looking for Force-Velocity profile that maintains the max power, but changes
#' \code{F0} and \code{V0} so it maximized the take-off velocity calculated using \code{\link{get_samozino_take_off_velocity}}.
#' @param F0 Numeric value. Default 3000
#' @param V0 Numeric value. Default 4
#' @param bodyweight Numeric value. Default 75
#' @param push_off_distance Numeric value. Default 0.4
#' @param gravity_const Numeric value. Default 9.81
#' @return List
#' @export
#' @references
#' Samozino, Pierre. ‘A Simple Method for Measuring Lower Limb Force, Velocity and Power Capabilities During Jumping’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 65–96. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_4.
#'
#' ———. ‘Optimal Force-Velocity Profile in Ballistic Push-off: Measurement and Relationship with Performance’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 97–119. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_5.
#'
#' Samozino, Pierre, Jean-Benoît Morin, Frédérique Hintzy, and Alain Belli. ‘Jumping Ability: A Theoretical Integrative Approach’. Journal of Theoretical Biology 264, no. 1 (May 2010): 11–18. https://doi.org/10.1016/j.jtbi.2010.01.021.
#'
#' Samozino, Pierre, Enrico Rejc, Pietro Enrico Di Prampero, Alain Belli, and Jean-Benoît Morin. ‘Optimal Force–Velocity Profile in Ballistic Movements—Altius’: Medicine & Science in Sports & Exercise 44, no. 2 (February 2012): 313–22. https://doi.org/10.1249/MSS.0b013e31822d757a.
#' @examples
#' get_samozino_optimal_profile(F0 = 2500, V0 = 3.7, bodyweight = 85, push_off_distance = 0.42)
get_samozino_optimal_profile <- function(F0 = 3000,
V0 = 4,
bodyweight = 75,
push_off_distance = 0.4,
gravity_const = 9.81) {
# Dataframe to be forwarded to optim function
data <- data.frame(
F0 = F0,
V0 = V0,
bodyweight = bodyweight,
push_off_distance = push_off_distance,
gravity_constant = gravity_const
)
take_off_velocity <- get_samozino_take_off_velocity(F0, V0, bodyweight, push_off_distance, gravity_const)
# Probe TOV
take_off_velocity_v_increase <- get_samozino_take_off_velocity(F0, V0 * 1.1, bodyweight, push_off_distance, gravity_const)
take_off_velocity_f_increase <- get_samozino_take_off_velocity(F0 * 1.1, V0, bodyweight, push_off_distance, gravity_const)
# function to be returned to optim
opt_jump_func <- function(par, data) {
new_F0 <- data$F0 / par[1]
new_V0 <- data$V0 * par[1]
take_off_velocity <- get_samozino_take_off_velocity(
new_F0,
new_V0,
data$bodyweight,
data$push_off_distance,
data$gravity_const
)
return(1 / take_off_velocity)
}
# ------------------------
# Find optimal parameters
upper_bound <- (F0 / bodyweight) / gravity_const
get_optim_model <- function() {
tryCatch(
{
stats::optim(par = 1, fn = opt_jump_func, data = data, method = "Brent", lower = 0, upper = upper_bound)
},
error = function(cond) {
return(list(par = NA, value = NA))
},
warning = function(cond) {
return(list(par = NA, value = NA))
}
)
}
results <- get_optim_model()
# Save the results
Sfv <- get_slope(F0, V0)
Sfv_rel <- Sfv / bodyweight
optimal_F0 <- F0 / results$par[1]
optimal_V0 <- V0 * results$par[1]
optimal_Sfv <- get_slope(optimal_F0, optimal_V0)
optimal_Sfv_rel <- optimal_Sfv / bodyweight
optimal_take_off_velocity <- 1 / results$value
optimal_height <- get_height(optimal_take_off_velocity, gravity_const)
optimal_Pmax <- get_max_power(optimal_F0, optimal_V0)
height <- get_height(take_off_velocity, gravity_const)
df <- list(
F0 = F0,
F0_rel = F0 / bodyweight,
V0 = V0,
Pmax = get_max_power(F0, V0),
Pmax_rel = get_max_power(F0, V0) / bodyweight,
Sfv = Sfv,
Sfv_rel = Sfv_rel,
take_off_velocity = take_off_velocity,
height = height,
optimal_F0 = optimal_F0,
optimal_F0_rel = optimal_F0 / bodyweight,
optimal_V0 = optimal_V0,
optimal_height = optimal_height,
optimal_height_diff = optimal_height - height,
optimal_height_ratio = optimal_height / height,
optimal_Pmax = optimal_Pmax,
optimal_Pmax_rel = optimal_Pmax / bodyweight,
optimal_take_off_velocity = optimal_take_off_velocity,
optimal_take_off_velocity_diff = optimal_take_off_velocity - take_off_velocity,
optimal_take_off_velocity_ratio = optimal_take_off_velocity / take_off_velocity,
optimal_Sfv = optimal_Sfv,
optimal_Sfv_rel = optimal_Sfv_rel,
Sfv_perc = (Sfv / optimal_Sfv) * 100,
FV_imbalance = abs(1 - (Sfv / optimal_Sfv)) * 100,
probe_IMB = (take_off_velocity_v_increase - take_off_velocity) / (take_off_velocity_f_increase - take_off_velocity) * 100
)
return(df)
}
#' Get All Samozino profiles
#'
#' \code{get_all_samozino_profiles} returns theoretical and practical Samozino profiles using \code{profile_data}
#' returned from the \code{\link{vj_profile}} and \code{\link{get_samozino_optimal_profile}} functions
#' @param profile_data Data frame returned from \code{\link{vj_profile}} function
#' @return List with two elements: list of profiles and long data frame
#' @export
#' @references
#' Samozino, Pierre. ‘A Simple Method for Measuring Lower Limb Force, Velocity and Power Capabilities During Jumping’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 65–96. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_4.
#'
#' ———. ‘Optimal Force-Velocity Profile in Ballistic Push-off: Measurement and Relationship with Performance’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 97–119. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_5.
#'
#' Samozino, Pierre, Jean-Benoît Morin, Frédérique Hintzy, and Alain Belli. ‘Jumping Ability: A Theoretical Integrative Approach’. Journal of Theoretical Biology 264, no. 1 (May 2010): 11–18. https://doi.org/10.1016/j.jtbi.2010.01.021.
#'
#' Samozino, Pierre, Enrico Rejc, Pietro Enrico Di Prampero, Alain Belli, and Jean-Benoît Morin. ‘Optimal Force–Velocity Profile in Ballistic Movements—Altius’: Medicine & Science in Sports & Exercise 44, no. 2 (February 2012): 313–22. https://doi.org/10.1249/MSS.0b013e31822d757a.
#' @examples
#' fv_profile <- vj_profile(mass = 75)
#' all_samozino_profiles <- get_all_samozino_profiles(fv_profile)
#' all_samozino_profiles$data_frame
get_all_samozino_profiles <- function(profile_data) {
# Theoretical Samozino profile
# Uses mean velocity of the profile
jump_profile <- get_FV_profile(
profile_data,
force = "mean_GRF_over_distance",
velocity = "mean_velocity"
)
samozino_theoretical_profile <- get_samozino_optimal_profile(
F0 = jump_profile$F0,
V0 = jump_profile$V0,
bodyweight = profile_data$bodyweight[1],
push_off_distance = profile_data$push_off_distance[1],
gravity_const = profile_data$gravity_const[1]
)
# Practical Samozino profile
# Uses half of take-off velocity as mean velocity
# This is easier to measure without laboratory conditions
jump_profile <- get_FV_profile(
profile_data,
force = "mean_GRF_over_distance",
velocity = "mean_velocity_as_TOV_half"
)
samozino_practical_profile <- get_samozino_optimal_profile(
F0 = jump_profile$F0,
V0 = jump_profile$V0,
bodyweight = profile_data$bodyweight[1],
push_off_distance = profile_data$push_off_distance[1],
gravity_const = profile_data$gravity_const[1]
)
# Bind them together
profiles_list <- list(
samozino_theoretical_profile = samozino_theoretical_profile,
samozino_practical_profile = samozino_practical_profile
)
profiles_df <- dplyr::bind_rows(profiles_list, .id = "profile")
profiles_df <- tidyr::gather(profiles_df, "metric", "value", -1, na.rm = TRUE)
profiles_df$profile <- factor(
profiles_df$profile,
levels = c(
"samozino_practical_profile",
"samozino_theoretical_profile"
),
labels = c(
"Samozino practical profile",
"Samozino theoretical profile"
)
)
# Sort data frame
profiles_df <- profiles_df[order(profiles_df$profile), ]
return(list(
list = profiles_list,
data_frame = profiles_df
))
}
#' Get Samozino Jump Metrics
#'
#' \code{get_samozino_jump_metrics} return mean force, mean velocity and mean power using simple method explained in
#' the references.
#' @param mass Numeric vector. Default 75
#' @param push_off_distance Numeric vector. Default 0.4
#' @param height Numeric vector. Jump height. Default 0.5
#' @param gravity_const Numeric vector. Default 9.81
#' @return List with \code{mass}, \code{push_off_distance}, \code{height}, \code{gravity_const}, \code{mean_GRF_over_distance},
#' \code{mean_velocity}, \code{take_off_velocity}, and \code{mean_power}
#' @references
#' Samozino, Pierre. ‘A Simple Method for Measuring Lower Limb Force, Velocity and Power Capabilities During Jumping’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 65–96. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_4.
#'
#' ———. ‘Optimal Force-Velocity Profile in Ballistic Push-off: Measurement and Relationship with Performance’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 97–119. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_5.
#'
#' Samozino, Pierre, Jean-Benoît Morin, Frédérique Hintzy, and Alain Belli. ‘Jumping Ability: A Theoretical Integrative Approach’. Journal of Theoretical Biology 264, no. 1 (May 2010): 11–18. https://doi.org/10.1016/j.jtbi.2010.01.021.
#'
#' Samozino, Pierre, Enrico Rejc, Pietro Enrico Di Prampero, Alain Belli, and Jean-Benoît Morin. ‘Optimal Force–Velocity Profile in Ballistic Movements—Altius’: Medicine & Science in Sports & Exercise 44, no. 2 (February 2012): 313–22. https://doi.org/10.1249/MSS.0b013e31822d757a.
#' @export
#' @examples
#' get_samozino_jump_metrics(
#' mass = 75,
#' push_off_distance = 0.43,
#' height = 0.45
#' )
get_samozino_jump_metrics <- function(mass = 75,
push_off_distance = 0.4,
height = 0.5,
gravity_const = 9.81) {
mean_GRF_over_distance <- mass * gravity_const * (height / push_off_distance + 1)
mean_velocity <- sqrt(gravity_const * height / 2)
mean_power <- mean_GRF_over_distance * mean_velocity
return(list(
mass = mass,
push_off_distance = push_off_distance,
height = height,
gravity_const = gravity_const,
mean_GRF_over_distance = mean_GRF_over_distance,
mean_velocity = mean_velocity,
# this is equal to sqrt(2 * gravity_const * height),
take_off_velocity = mean_velocity * 2,
mean_power = mean_power
))
}
#' Probe Samozino Take-off Velocity
#'
#' \code{probe_samozino_take_off_velocity} probes results of the \code{\link{get_samozino_take_off_velocity}} function by varying
#' \code{F0}, \code{V0}, and \code{bodyweight} parameters
#' @param F0 Numeric vector. Default 3000
#' @param V0 Numeric vector. Default 4
#' @param bodyweight Numeric vector. Default 75
#' @param push_off_distance Numeric vector. Default 0.4
#' @param gravity_const Numeric vector. Default 9.81
#' @param change_ratio Numeric vector indicating probing change ratios
#' @param aggregate How should \code{\link{get_samozino_take_off_velocity}} output be aggregated?
#' Default is "raw". Other options involve "ratio" and "diff" which use initial
#' output values
#' @return Probing data frame
#' @export
#' @examples
#' require(ggplot2)
#'
#' samozino_probe_data <- probe_samozino_take_off_velocity(
#' F0 = 3000,
#' V0 = 3.5,
#' push_off_distance = 0.4,
#' bodyweight = 75,
#' change_ratio = seq(0.8, 1.2, length.out = 1001)
#' )
#'
#' ggplot(
#' samozino_probe_data,
#' aes(
#' x = change_ratio,
#' y = take_off_velocity,
#' color = probing
#' )
#' ) +
#' geom_line()
probe_samozino_take_off_velocity <- function(F0 = 3000,
V0 = 4,
bodyweight = 75,
push_off_distance = 0.4,
gravity_const = 9.81,
change_ratio = seq(0.9, 1.1, length.out = 3),
aggregate = "raw") {
get_probing_data(
args_list = list(F0 = F0, V0 = V0, bodyweight = bodyweight),
probe_func = function(...) list(take_off_velocity = get_samozino_take_off_velocity(...)),
change_ratio = change_ratio,
aggregate = aggregate,
push_off_distance = push_off_distance,
gravity_const = gravity_const
)
}
#' Get Samozino Profile
#'
#' \code{get_samozino_profile} returns Samozino model estimated from known \code{bodyweight}, \code{push_off_distance},
#' \code{mean_GRF_over_distance}, \code{mean_velocity} and \code{gravity_const}.
#' @param bodyweight Numeric value
#' @param push_off_distance Numeric value
#' @param mean_GRF_over_distance Numeric vector
#' @param mean_velocity Numeric vector
#' @param gravity_const Numeric value
#' @return Object returned from \code{\link{get_samozino_optimal_profile}} with addition of RSE and R_Squared elements
#' @references
#' Samozino, Pierre. ‘A Simple Method for Measuring Lower Limb Force, Velocity and Power Capabilities During Jumping’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 65–96. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_4.
#'
#' ———. ‘Optimal Force-Velocity Profile in Ballistic Push-off: Measurement and Relationship with Performance’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 97–119. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_5.
#'
#' Samozino, Pierre, Jean-Benoît Morin, Frédérique Hintzy, and Alain Belli. ‘Jumping Ability: A Theoretical Integrative Approach’. Journal of Theoretical Biology 264, no. 1 (May 2010): 11–18. https://doi.org/10.1016/j.jtbi.2010.01.021.
#'
#' Samozino, Pierre, Enrico Rejc, Pietro Enrico Di Prampero, Alain Belli, and Jean-Benoît Morin. ‘Optimal Force–Velocity Profile in Ballistic Movements—Altius’: Medicine & Science in Sports & Exercise 44, no. 2 (February 2012): 313–22. https://doi.org/10.1249/MSS.0b013e31822d757a.
#' @export
#' @examples
#' require(tidyverse)
#' data("testing_data")
#'
#' testing_data <- testing_data %>%
#' mutate(
#' height = vjsim::get_height_from_aerial_time(aerial_time),
#' total_load = bodyweight + external_load
#' )
#'
#' jump_metric <- function(data) {
#' samozino_metrics <- vjsim::get_samozino_jump_metrics(
#' mass = data$bodyweight + data$external_load,
#' push_off_distance = data$push_off_distance,
#' height = data$height
#' )
#' return(as.data.frame(samozino_metrics))
#' }
#'
#'
#' testing_data <- testing_data %>%
#' # Need to add bodyweight so it is kept in the output
#' group_by(athlete, bodyweight) %>%
#' do(jump_metric(.))
#'
#' samozino_profile <- function(data) {
#' samozino_data <- vjsim::get_samozino_profile(
#' bodyweight = data$bodyweight,
#' push_off_distance = data$push_off_distance,
#' mean_GRF_over_distance = data$mean_GRF_over_distance,
#' mean_velocity = data$mean_velocity
#' )
#'
#' return(as.data.frame(samozino_data))
#' }
#'
#' testing_data_samozino <- testing_data %>%
#' # Need to add bodyweight so it is kept in the output
#' group_by(athlete, bodyweight) %>%
#' do(samozino_profile(.))
#'
#' testing_data_samozino
get_samozino_profile <- function(bodyweight,
push_off_distance,
mean_GRF_over_distance,
mean_velocity,
gravity_const = 9.81) {
# Check if any of the parameters is NA and return a list with NA
if (any(
is.na(bodyweight),
is.na(push_off_distance),
is.na(mean_GRF_over_distance),
is.na(mean_velocity),
is.na(gravity_const)
)) {
return(lapply(
get_samozino_optimal_profile(
F0 = 5000,
V0 = 4,
bodyweight = 100,
push_off_distance = 0.4,
gravity_const = 10
),
function(x) {
NA
}
))
}
profile_data <- data.frame(
bodyweight = bodyweight,
mean_GRF_over_distance = mean_GRF_over_distance,
mean_velocity = mean_velocity
)
jump_profile <- get_FV_profile(
profile_data,
force = "mean_GRF_over_distance",
velocity = "mean_velocity"
)
# Calculate residual standard error and R^2
predicted_mean_velocity <- jump_profile$V0 + mean_GRF_over_distance / jump_profile$Sfv
RSE <- sqrt(sum((predicted_mean_velocity - mean_velocity)^2) / (length(mean_velocity) - 2))
R_squared <- stats::cor(predicted_mean_velocity, mean_velocity)^2
samozino_profile <- get_samozino_optimal_profile(
F0 = jump_profile$F0,
V0 = jump_profile$V0,
bodyweight = bodyweight[1],
push_off_distance = push_off_distance[1],
gravity_const = gravity_const[1]
)
samozino_profile$RSE <- RSE
samozino_profile$R_squared <- R_squared
return(samozino_profile)
}
#' Make Samozino Profile
#'
#' \code{make_samozino_profile} generates Samozino profile from squat jump data. When both \code{aerial_time} and
#' \code{height} are forwarded to the function, only \code{height} is used to estimate mean GRF.
#'
#' @param bodyweight Numeric value
#' @param push_off_distance Numeric value
#' @param external_load Numeric vector
#' @param height Numeric vector
#' @param aerial_time Numeric vector
#' @param gravity_const Numeric vector. Default 9.81
#' @param plot TRUE/FALSE. Default is TRUE
#' @return List of Samozino profile parameters
#' @export
#' @references
#' Samozino, Pierre. ‘A Simple Method for Measuring Lower Limb Force, Velocity and Power Capabilities During Jumping’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 65–96. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_4.
#'
#' ———. ‘Optimal Force-Velocity Profile in Ballistic Push-off: Measurement and Relationship with Performance’. In Biomechanics of Training and Testing, edited by Jean-Benoit Morin and Pierre Samozino, 97–119. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-05633-3_5.
#'
#' Samozino, Pierre, Jean-Benoît Morin, Frédérique Hintzy, and Alain Belli. ‘Jumping Ability: A Theoretical Integrative Approach’. Journal of Theoretical Biology 264, no. 1 (May 2010): 11–18. https://doi.org/10.1016/j.jtbi.2010.01.021.
#'
#' Samozino, Pierre, Enrico Rejc, Pietro Enrico Di Prampero, Alain Belli, and Jean-Benoît Morin. ‘Optimal Force–Velocity Profile in Ballistic Movements—Altius’: Medicine & Science in Sports & Exercise 44, no. 2 (February 2012): 313–22. https://doi.org/10.1249/MSS.0b013e31822d757a.
#' @examples
#' require(tidyverse)
#'
#' data("testing_data")
#'
#' with(
#' filter(testing_data, athlete == "Jack"),
#' make_samozino_profile(
#' bodyweight = bodyweight,
#' push_off_distance = push_off_distance,
#' external_load = external_load,
#' aerial_time = aerial_time,
#' plot = TRUE
#' )
#' )
make_samozino_profile <- function(bodyweight,
push_off_distance,
external_load,
height,
aerial_time,
gravity_const = 9.81,
plot = TRUE) {
# Check if both height and aerial_time are used
if (!missing(height) & !missing(aerial_time)) {
warning("Please use either height or aerial time as a parameter. Using height to model", call. = FALSE)
}
# If height missing, use aerial time to create it
if (missing(height)) {
height <- get_height_from_aerial_time(aerial_time, gravity_const)
}
# Get Force-Velocity profile
samozino_metrics <- get_samozino_jump_metrics(
mass = bodyweight + external_load,
push_off_distance = push_off_distance,
height = height,
gravity_const = gravity_const
)
# Get Samozino optimal profile
samozino_model <- get_samozino_profile(
bodyweight = bodyweight,
push_off_distance = push_off_distance,
mean_GRF_over_distance = samozino_metrics$mean_GRF_over_distance,
mean_velocity = samozino_metrics$mean_velocity,
gravity_const = gravity_const
)
# Create plot
if (plot) {
# Define function to calculate TOV from mean force
get_tov <- function(mass, gravity_const, mean_force, push_off_distance) {
sqrt((2 * push_off_distance * (mean_force - mass * gravity_const)) / mass)
}
plot_data <- data.frame(
group = rep(1:2, each = 2),
x = c(samozino_model$F0, 0),
y = c(0, samozino_model$V0)
)
plot_data_optimal <- data.frame(
group = rep(1:2, each = 2),
x = c(samozino_model$optimal_F0, 0),
y = c(0, samozino_model$optimal_V0)
)
mean_force_df <- expand.grid(
mass = bodyweight,
gravity_const = gravity_const,
push_off_distance = push_off_distance,
mean_GRF_over_distance = seq(min(bodyweight) * gravity_const, max(samozino_model$F0, samozino_model$optimal_F0))
)
mean_force_df$MV <- get_tov(
mass = bodyweight,
gravity_const = gravity_const,
mean_force = mean_force_df$mean_GRF_over_distance,
push_off_distance = push_off_distance
) / 2
gg <- ggplot2::ggplot() +
cowplot::theme_cowplot(8) +
ggplot2::geom_line(
ggplot2::aes(
x = mean_force_df$mean_GRF_over_distance,
y = mean_force_df$MV
),
alpha = 0.8,
color = "grey"
) +
ggplot2::geom_point(
ggplot2::aes(
x = samozino_metrics$mean_GRF_over_distance,
y = samozino_metrics$mean_velocity
),
alpha = 0.8
) +
ggplot2::geom_line(
ggplot2::aes(
x = plot_data$x,
y = plot_data$y
),
alpha = 0.8
) +
ggplot2::geom_line(
ggplot2::aes(
x = plot_data_optimal$x,
y = plot_data_optimal$y
),
alpha = 0.8,
linetype = "dashed"
) +
ggplot2::xlab("Mean GRF [N]") +
ggplot2::ylab("Mean Velocity [m/s]") +
ggplot2::ggtitle(
"Samozino profile",
paste(
"F0 = ", round(samozino_model$F0, 0), "N",
"; V0 = ", round(samozino_model$V0, 2), "m/s",
"; Pmax = ", round(samozino_model$Pmax, 0), "W",
"; Sfv = ", round(samozino_model$Sfv, 0),
"; Height = ", round(samozino_model$height, 2), "m",
"; RSE = ", round(samozino_model$RSE, 2), "m/s",
"; R2 = ", round(samozino_model$R_squared, 2),
"\n",
"Optimal: ",
"F0 = ", round(samozino_model$optimal_F0, 0), "N",
"; V0 = ", round(samozino_model$optimal_V0, 2), "m/s",
"; Pmax = ", round(samozino_model$optimal_Pmax, 0), "W",
"; Sfv = ", round(samozino_model$optimal_Sfv, 0),
"; Height = ", round(samozino_model$optimal_height, 2), "m",
"\n",
"Sfv% = ", round(samozino_model$Sfv_perc, 2),
"; FVimb = ", round(samozino_model$FV_imbalance, 2),
sep = ""
)
)
plot(gg)
}
return(samozino_model)
}
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