In MarcoKlH/afpt-r: Tools for Modelling of Animal Flight Performance

library(afpt)

In this example we will look at how to compute flight performance for a set of birds. We will use the birds described in @Hedenstrom1992a. The pacakge has limited capabilities for handling multiple birds in a data.frame. We first load the data set in the workspace. This prepared data set already has a format recognized by the bird constructor, and can therefore be used directly as Bird(climbing_birds).

data(climbing_birds) #  Load climbing bird data set

climbing_birds <- climbing_birds#[seq(1,15,3),]
myBirds <- Bird(climbing_birds)

myBirds$coef.profileDragLiftFactor[myBirds$name=='Mute swan'] = 0 
# we have to assume that swans has specialized aerofoil, as it otherwise won't be able to fly
# this may be true for other birds too, and should be investigated further...

myBirds[c('name','massTotal','wingSpan','wingArea','wingbeatFrequency')]

As this data set was used in relation to climb performance, we will use the function findMaximumClimbRate():

myBirds$powerAvailable <- computeAvailablePower(myBirds)
climbperf <- findMaximumClimbRate(myBirds,maximumPower = myBirds$powerAvailable,strokeplane=20)
climbperf[c('speed','climbRate','frequency','amplitude')]

Without prescribing an airspeed, this function searches for the airspeed that maximizes climbrate. Climbrate is computed by adding a component of the weight, $W\sin\gamma$, to the drag (here $W$ is the weight, and $\gamma$ is the climb angle), and then finding the climb angle at which the aerodynamic power requirement matches the available power. This gives a slightly different result than the traditional method of converting the power margin at minimum power speed directly, because the propulsive efficiency depends on the thrust requirement. For comparison:

minpower <- findMinimumPowerSpeed(myBirds,strokeplane=20)
climbperf.trad <- data.frame( # compute traditional climb performance
  speed = minpower$speed,
  climbRate = (myBirds$powerAvailable-minpower$power)/myBirds$massTotal/9.81
)

climbperf[c('speed','climbRate')]/climbperf.trad # compare

The climb performance of these birds was observed by radar tracking. The model can predict the maximum climbrate for these observed speeds:

myBirds$climbSpeed <- climbing_birds$climbSpeed # attach observed climb speeds to the bird data
climbperf2 <- findMaximumClimbRate(
  myBirds,computeAvailablePower(myBirds),
  speed=myBirds$climbSpeed, # specify observed climb speeds
  strokeplane=20
)

climbperf2[c('speed','climbRate','frequency','amplitude','strokeplane')]

par(mar=c(3.1,3.1,0.4,1.1),mgp=c(1.9,.7,0),cex=0.75)


plot(climbperf$speed,climbperf$climbRate,col='red3',xlim=c(5,21),ylim=c(-.5,2.1),xlab = NA, ylab = NA)
par(new=TRUE)
plot(climbing_birds$climbSpeed,climbing_birds$climbRate,xlim=c(5,21),ylim=c(-.5,2.1),xlab=NA, ylab=NA, axes=FALSE)
arrows(x0 = climbperf$speed, y0 = climbperf$climbRate, x1 = climbing_birds$climbSpeed, y1 = climbing_birds$climbRate,length=0.15,angle=10,col='grey90')
text(climbperf$speed-.5,climbperf$climbRate-.1,climbperf$number)
mtext(side = 1, line = 2,'Airspeed (m/s)')
mtext(side = 2, line = 2,'Climb rate (m/s)')

plot(climbperf2$speed,climbperf2$climbRate,col='green3',xlim=c(9,21),ylim=c(-.1,1.8),xlab = NA, ylab = NA)
par(new=TRUE)
plot(climbing_birds$climbSpeed,climbing_birds$climbRate,xlim=c(9,21),ylim=c(-.1,1.8),xlab=NA, ylab=NA, axes=FALSE)
arrows(x0 = climbperf2$speed, y0 = climbperf2$climbRate, x1 = climbing_birds$climbSpeed, y1 = climbing_birds$climbRate,length=0.15,angle=10,col='grey90')
text(climbperf2$speed-.5,climbperf2$climbRate-.1,climbperf2$number)
mtext(side = 1, line = 2,'Airspeed (m/s)')
mtext(side = 2, line = 2,'Climb rate (m/s)')

par(mar=c(3.1,3.1,0.4,1.1),mgp=c(1.9,.7,0),cex=0.75)

plot(climbing_birds$climbSpeed/climbperf$speed-1,
     climbing_birds$climbRate-climbperf$climbRate,
     xlim = c(-.15,1),ylim = c(-1.34,.8),
     col='red3',xlab = NA, ylab = NA)
arrows(x0 = climbing_birds$climbSpeed/climbperf$speed-1,
       y0 = climbing_birds$climbRate-climbperf$climbRate,
       x1 = 0, y1 = climbing_birds$climbRate-climbperf2$climbRate,
       length=0.1,angle=10,col='grey90')

abline(v=0,col='grey')
abline(h=0,col='grey')

text(climbing_birds$climbSpeed/climbperf$speed-1-.05,
     climbing_birds$climbRate-climbperf$climbRate-.05,
     climbperf$number)

mtext(side = 1, line = 2,'Airspeed (obs./pred. - 1)')
mtext(side = 2, line = 2,'Climb rate (obs. - pred.)')