In this example we will look at how to compute flight performance for a set of birds. We will use the birds described in Hedenström and Alerstam (1992). 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')]## name massTotal wingSpan wingArea wingbeatFrequency
## 1 Mute swan 10.56000 2.23 0.540532609 3.5
## 2 Greylag goose 3.57500 1.64 0.316423529 3.8
## 3 Eider 1.79300 0.94 0.105190476 7.0
## 4 Red-throated diver 1.36400 1.11 0.100991803 5.5
## 5 Brent goose 1.36400 1.15 0.123598131 5.0
## 6 Curlew 0.79200 0.90 0.120895522 5.5
## 7 Wigeon 0.71500 0.80 0.078048780 6.5
## 8 Wood pigeon 0.53900 0.78 0.093600000 5.8
## 9 Oystercatcher 0.52800 0.83 0.079183908 5.7
## 10 Arctic tern 0.12100 0.80 0.057142857 4.1
## 11 Song thrush 0.06588 0.34 0.019266667 10.1
## 12 Dunlin 0.04998 0.40 0.014545455 8.1
## 13 Swift 0.04070 0.45 0.015340909 6.8
## 14 Chaffinch 0.02204 0.26 0.012754717 9.8
## 15 Siskin 0.01140 0.21 0.007474576 11.2As 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')]## speed climbRate frequency amplitude
## 1 17.437234 0.27598741 3.5 28.95810
## 2 16.085625 0.07381682 3.8 33.26917
## 3 17.923576 0.27167314 7.0 41.48678
## 4 15.314955 0.41368742 5.5 39.44518
## 5 14.640349 0.40712680 5.0 39.08424
## 6 13.151185 0.64786121 5.5 43.73877
## 7 14.122421 0.68897362 6.5 45.47488
## 8 12.467322 0.74436634 5.8 46.58590
## 9 12.320401 0.76769487 5.7 45.44499
## 10 7.033862 0.89175445 4.1 48.30411
## 11 9.882467 1.77672285 10.1 65.18206
## 12 8.455751 1.40921938 8.1 59.83829
## 13 7.277247 1.46502960 6.8 60.39518
## 14 7.546147 1.76797674 9.8 71.69574
## 15 5.013951 2.30762726 11.2 83.54983Without 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## speed climbRate
## 1 1.0187631 0.8421719
## 2 1.0050750 0.7932620
## 3 1.0154745 0.7406871
## 4 1.0263884 0.7817314
## 5 1.0282111 0.7873369
## 6 1.0512358 0.7836472
## 7 1.0493672 0.7673626
## 8 1.0623172 0.7776499
## 9 1.0618622 0.7891940
## 10 1.1104072 0.8354703
## 11 1.1556532 0.7702182
## 12 1.1405148 0.7948562
## 13 1.1547435 0.8160012
## 14 1.1989975 0.7780880
## 15 0.9010589 0.8540825The 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')]## speed climbRate frequency amplitude strokeplane
## 1 16.7 0.27277198 3.5 28.95211 20
## 2 15.9 0.07353519 3.8 33.26125 20
## 3 16.9 0.26065227 7.0 41.39131 20
## 4 17.9 0.34735164 5.5 39.51922 20
## 5 16.4 0.37621073 5.0 39.13836 20
## 6 14.9 0.61239513 5.5 43.78936 20
## 7 20.3 0.25871426 6.5 45.51540 20
## 8 15.5 0.62966622 5.8 46.62685 20
## 9 13.6 0.74683532 5.7 45.47474 20
## 10 9.9 0.74390078 4.1 47.88441 20
## 11 12.4 1.63959372 10.1 64.96896 20
## 12 13.9 0.80656514 8.1 59.09936 20
## 13 10.0 1.29593370 6.8 59.79491 20
## 14 11.2 1.39915854 9.8 70.73258 20
## 15 13.4 0.77087587 11.2 75.39675 20
Climb performance predicted and observed – Birds in the top-left quadrant are predicted at nearly the observed flight speed, but were observed climbing faster than alowed by the model, indicating their drag is estimated too high. The birds in the top-right quadrant are flying at a higher flight speed than predicted and their climbrate is also higher, suggesting most likely body drag is estimated too high. The birds in the lower-right quadrant may just have been observed performing a sub-optimal climb. Alternatively particularly their lift dependent drag may be under predicted in the model. The arrows indicate the climb rate predicted by the model for the observed flight speed. In this case all positive values indicate the drag in the model is too high.
Hedenström A, Alerstam T. 1992. Climbing performance of migrating birds as a basis for estimating limits for fuel-carrying capacity and muscle work. J. Exp. Biol. 164, 19–38.