[chronojump] Sprint analysis. pmax.fitted calculated analytically.

[Xavier Padullés <xpadulles src gnome org>]

commit 2855f3dc8ac80197313a90cfa648723319f4c4c8
Author: Xavier Padullés <x padulles gmail com>
Date:   Mon Nov 27 09:16:44 2017 +0100

    Sprint analysis. pmax.fitted calculated analytically.

 r-scripts/sprintUtil.R |    6 +++---
 1 files changed, 3 insertions(+), 3 deletions(-)
---
diff --git a/r-scripts/sprintUtil.R b/r-scripts/sprintUtil.R
index d8c96d6..782a553 100644
--- a/r-scripts/sprintUtil.R
+++ b/r-scripts/sprintUtil.R
@@ -49,9 +49,6 @@ getDynamicsFromSprint <- function(K, Vmax, Mass, Temperature = 25, Height , Vw =
         a.fitted = Vmax*K*exp(-K*time)
         f.fitted = Mass*a.fitted + Ka*(v.fitted - Vw)^2
         p.fitted = f.fitted * v.fitted
-        pmax.fitted = max(p.fitted)                 #TODO: Make an interpolation between the two closest 
points
-        pmax.rel.fitted = pmax.fitted / Mass
-        tpmax.fitted = time[which.max(p.fitted)]
         
         #Modeling F-v with the wind friction.
         # a(v) = Vmax*K*(1 - v/Vmax)
@@ -67,6 +64,9 @@ getDynamicsFromSprint <- function(K, Vmax, Mass, Temperature = 25, Height , Vw =
         V0 = -F0/fvModel$coefficients[2]             # Similar to Vmax.fitted. V0 is the interception of the 
linear regression with the horizontal axis
         pmax.lm = V0 * F0/4                          # Max Power Using the linear regression. The maximum is 
found in the middle of the parabole p(v)
         pmax.rel.lm = pmax.lm / Mass
+        pmax.fitted = fmax.fitted * Vmax / 4         # Obtained from the function P(v) = F(v) * v. It is a 
parabele. The apex is in Vmax/2
+        pmax.rel.fitted = pmax.fitted / Mass
+        tpmax.fitted = log(2) / K                    # Obtained from P'(t) = 0
         
         return(list(Mass = Mass, Height = Height, Temperature = Temperature, Vw = Vw, Ka = Ka, K.fitted = K, 
Vmax.fitted = Vmax,
                     amax.fitted = amax.fitted, fmax.fitted = fmax.fitted, fmax.rel.fitted = fmax.rel.fitted, 
sfv.fitted = sfv.fitted, sfv.rel.fitted = sfv.rel.fitted,