Lecture 4

.title[
# Lecture 4
]
.subtitle[
## Terrestrial Locomotion III
]
.author[
### Dr. Christopher Kenaley
]
.institute[
### Boston College
]
.date[
### 2024/1/25
]

---

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- Consider a controversy

- Unravel scaling in locomotion

- AME assessment and revision proecess
]

.pull-right[
![](https://www.sciencenewsforstudents.org/wp-content/uploads/2019/11/EasternGraySquirrel-cropped-800x428.jpg)
![](https://i1.wp.com/blog.bookyourhunt.com/wp-content/uploads/2018/05/running-antelope-2-e1526150586788.jpg?fit=1585%2C759&ssl=1)

]

---
class: top

# First, a controversy

<img src="img/pistorius.jpg" width="550" />
 ]

---

# First, a controversy

<img src="img/musclesprings.jpg" width="500" />
]

![](https://www.acs.psu.edu/drussell/Demos/SHO/damp.gif)

]

]

---
class: top

# Scaling in locomotion

.pull-left[
- Stress:
  `$$\sigma=F/A$$`
- Strain is proportional to stress according to the elastic (Young's) modulus (*E*).

- With length (size), mass scales cubically while `$A$` scales to the square.

- *F= M x g*, so forces (GRF in particular), increase with decreased duty factor

- Bones are similarly stiff across terrestrial tetrapods

- Problems?
]

.pull-right[
![](https://boneclones.com/images/store-product/product-1572-main-main-big-1415043795.jpg)
1= Horse, 12= Flying lemur
]

---
class: top

# Scaling in locomotion

.pull-left[
- Capacity of a bone to support/generate force decreases relative to the increase in mass or weight of the animal.

- Under geometric similarity (isometry), shape remains constant so that expected increase in withstanding increasing skeletal stress is given by:

$$ \frac{F}{A} \propto \frac{M^{1.0}}{M^{2/3}} \propto M^{1/3}$$
- This is the ability to withstand a fracture!
]

-  `$\frac{F}{A} \propto M^{0.28}$`, so some allometry in dimensions

- no terrestrial mammals or birds should be able to run/gallop > 20 kg in body mass

- would exceed compressive fracture strength of -240 MPa!
]

---

# Scaling in locomotion

### Scaling in bone dimenstions

]

---
class: top

# Scaling in locomotion

### Scaling in EMA

<img src="img/emascale.png" width="250" />
 ]
 
 
---
class: top

# Scaling in locomotion

### Scaling in EMA

<img src="img/emascalinglimbs.png" width="450" />
 ]
 
 .footnote[
 `$$EMA=r/R$$`
 ]
 
---
class: top

# Scaling in locomotion

### Scaling in EMA

<img src="https://vhmsscience.weebly.com/uploads/1/2/7/6/12762866/3006320_orig.jpg" width="450" />
 ]
 
 .footnote[
 `$$EMA=r/R$$`
 ]
 
 
---
class: top

# Scaling in locomotion

### Scaling in EMA

<img src="https://www.researchgate.net/profile/Taylor_Dick/publication/312307421/figure/fig2/AS:450892588687361@1484512578260/Effect-of-body-size-and-posture-on-limb-EMA-A-Hindlimb-EMA-scaling-for-mammals-data.png" width="650" />
 ]
 
 .footnote[
 `$$EMA=r/R$$`
 ]

---

# Thanks!

Slides created via the R package [**xaringan**](https://github.com/yihui/xaringan).