Tag: Toronto

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Baseball throw from the CN Tower — fun physics

The question

A Sportsnet reporter, Shawn McKenzie, recently asked a question that’s surprisingly tricky to answer:

could someone standing on the CN Tower throw a baseball all the way to third base at the SkyDome? 

From the CN Tower’s observation deck or EdgeWalk the baseball field looks close. Close enough to be a tempting target for a baseball throw…

Sportsnet turned the question into a great 5-minute video you can watch on YouTube:

(It’s also on Instagram here: https://www.instagram.com/p/DPRkyJ_EaRE/?igsh=Z2JuMXB5YzJhcWc1)

They included a short clip from what was a 30+ minute interview. We had a great conversation. For anyone interested, I thought I’d post more details about the physics of this scenario. 

(Personal aside: I worked as a host at the CN Tower during my undergrad degree. Hosts are the people who help visitors everywhere around the site – including the elevators rides. I enjoyed it. I recall looking down at the baseball field when the dome was open. However, it was also part of my job to ensure people didn’t throw objects from the lower observation deck, which used to be open to the air with a metal mesh…) 

Set up: the key information we need

To do this calculation, a few key facts need to be clarified: 

  • Characteristics of a baseball, 
  • Height, i.e., where the person is positioned at the CN Tower, 
  • Target distance, i.e., from the CN Tower to SkyDome’s third base, and
  • Speed of the throw, e.g., by a regular person and by a professional.

With this information we can estimate an answer.

A baseball’s physical characteristics are described by Major League Baseball official documentation here (section 3.01):

  • Mass: 5 to 5.25 ounces, which I converted to 145 grams
  • Circumference: 9 to 9.25 inches, which I converted to a radius of 3.7 cm
  • Shape: sphere, but not perfectly smooth. 

I used 365 m for the height of the person throwing the baseball. This is the height of the EdgeWalk, located on top of the observation section of the CN Tower. This seemed to be the most practical premise since it is where visitors can walk around outside. (I did the EdgeWalk years ago with a friend and I would do it again!)

263 meters was used as the distance of the target of third base. This is difficult to determine precisely and introduces a key uncertainty in answering the question. My first attempt at a rough estimate was to examine Google Maps and Google Earth. This suggested a distance between 200 m and 270 m. The dome is not open in most of the images but it’s worth noting that third base is the most distant of the bases from the CN Tower. Satellite images can be misleading due to viewing angles and distortions. A direct measurement is preferable. 

The segment producer measured the angle at the ground from third base (our target) to the EdgeWalk, which has a known height. From this, some trigonometry enables us to calculate the distance to be 263 m. This seems plausible and within the range suggested from the Google images. There are areas within the baseball diamond and stadium seats that would be closer to the CN Tower and easier to reach. Any distance greater than 200 m would likely be inside the SkyDome field and stands. As it turns out, that’s a much more achievable target.

Finally, we need to know how fast a person can throw a baseball. 

  • For a ‘regular person’, I used 90 km/h (25 m/s or 56 mph). This might be generous, but let’s think positively.
  • For a professional, I used 162 km/h (45 m/s), which is 100 mph. This seemed reasonable since the best pitch speed recorded in the current MLB is 170 km/h. This is roughly double the speed of a regular person. 

Also: throw angle 

The throw angle is also very important. For each throw speed, I used the angle that maximizes the horizontal distance. When throwing from a large height, the angle needs to be shallow (small) to maximize the horizontal distance.

Physics of the throw

The most important factors affecting the throw distance are gravity and air resistance.

Gravity is constant at the CN Tower: objects are accelerated downward at 9.81 m/s2. 

The density of air varies by height and in time. I used a typical value of 1.225 kg/m3. 

To illustrate the importance of these two factors in combination, imagine simply dropping the baseball from the EdgeWalk height of 365 m. 

Without considering air resistance, the ball would take about 8.5 seconds to reach the ground. However, once we add air resistance, the ball would take about 12 seconds. 

For comparison, dropping the ball from the same height on Mars, which has one third the gravity of Earth, would take 14 seconds to reach the ground without air resistance and 20 seconds with (Earth’s) air resistance.

Results: ignoring air resistance

A first year undergraduate physics student should be able to analyze the motion of the baseball and calculate the range without air resistance. This is not realistic. However, let’s start there.

This result shows that a professional can throw a baseball to third base. Perhaps even reaching the opposite side of the SkyDome stadium! A regular person could throw the baseball onto the field, but falls short of third base.

Now let’s consider the effect of air resistance. It may be more dramatic than some expect.

Results: with air resistance

There are a few challenges to doing this calculation with air resistance. 

The drag force created by the air is (very) speed dependent. As a result, you can’t do one calculation. Instead, I had (python language) code perform a calculation every 0.01 seconds of flight time to account for the changing speed and drag.

There is another decision: what model of drag should be used? I used the equation found in first year undergraduate physics textbooks:

For this situation, it is appropriate.

In the equation:

  • A is the area of the object in the direction of motion, a circle with a 3.7 cm radius
  • ρ is the density of the fluid (I’ve taken that to be 1.225 kg/m3)
  • v is the velocity of the object (baseball)
  • C is the drag coefficient. I used 0.38.

A typical C value for smooth spheres is 0.5. However, a baseball’s surface is rough and (significantly) it has raised stitching. The physics literature has measured a range of results for this value, e.g., Kensrud & Smith (2010), especially Figure 7, and Kagan & Nathan (2014). I used 0.38 as a conservative estimate.

Here are the results using those values:

Neither the regular person or the professional was able to reach the target. The professional might have been able to throw the baseball into the SkyDome, e.g., somewhere in the stands nearest to the CN Tower. That’s still impressive!

A logical question to consider is:

What throw speed IS necessary to reach third base, at a distance of 263 m?

Answer:

  • Without air resistance: 104 km/h (65 mph)
  • With air resistance: 300 km/h (186 mph)

It’s unrealistic for someone to throw a baseball at 300 km/h. These results suggest that someone might be able to throw a baseball from the CN Tower EdgeWalk inside the SkyDome. However, it’s very unlikely they could reach third base. 

Other solutions?

If 300 km/h seems impossible for a person, what else could we do?

Get higher

Additional height doesn’t help the horizontal range much. Even if you somehow stood on the very tip of the CN Tower spire (not recommended, especially in stormy weather), a height of 553 m doesn’t extend your throw by more than several meters. Air resistance and gravity are too much of a constraint. 

Spin

There is some range to be gained by ensuring the throw includes backspin. The magnus force created by spin can create a form of lift. Experimental analysis of backspin on baseball flights show that it is a difficult topic. Spin can help extend horizontal range (e.g., Nathan, 2008; Alaways & Hubbard, 2010; Kensrud & Smith, 2010). However, this also increases drag. The scale of the benefit would not be enough to make up the distance shortfall we saw in the earlier calculations.  

Moving to a different location

Since drag from air resistance is proportional to air density, we could move to a higher altitude, where the air density is lower. Moving the CN Tower is not realistic, but we could think about it for fun. 

The major city at the highest elevation I found was Lhasa, Tibet. It is at an altitude of 3.65 km and the air density is 0.83 kg/m3. However, it seems this change isn’t enough to meet our goal.  

What about the highest elevation in Canada?

Mount Logan in Yukon Territory has a height of 6 km. At this altitude, half of the atmosphere’s mass is beneath you! The air density is 0.6 kg/m3. 

Success!

The professional can throw the baseball and hit the target.

All we have to do is move the CN Tower and SkyDome to the peak of Mt. Logan. 

Change gravity

What if we could change gravity? e.g., to match the strength of gravity at the surface of the moon or on Mars?

If we magically changed to Martian gravity (3.7 m/s2), a regular person still falls short (173 m); however, the professional gets close enough that I think we can claim potential success: 247 m.

If we push further and consider Lunar gravity (1.625 m/s2), a regular person still falls short but likely reaches the inside of the stadium. Maybe the baseball even gets onto the field. 

Actual solution: wind

In the real world, a lucky gust of wind is the only way I think a professional pitcher can throw a baseball from the CN Tower EdgeWalk and it reaches third base in the SkyDome. The effect of wind is not trivial to calculate, and it varies in time and altitude. However a strong and sustained gust of wind could give the extra distance needed. 

But this situation raises a philosophical question: 

if the wind does much of the work, can we really say a person threw the ball to third base?

How far do you think you could throw a baseball from the CN Tower?

Further reading

There have been quite a few people interested in the physics of sports. Published papers about baseballs go back at least several decades. Here are a few highlights for anyone interested in reading physics literature about the details.

D. Kagan and A. M. Nathan, “Simplified models for the drag coefficient of a pitched baseball,” Phys. Teach. 52, 278–280 (2014). https://doi.org/10.1119/1.4872406

A. M. Nathan, “The effect of spin on the flight of a baseball,” Am. J. Phys. 76, 119–124 (2008). https://doi.org/10.1119/1.2805242

A. M. Nathan, “The physics of baseball: What’s the deal with drag?” Phys. Teach. 53, 332–335 (2015). https://doi.org/10.1119/1.4928349

L. W. Alaways and M. Hubbard, “Experimental determination of baseball spin and lift,” J. Sports Sci. 19, 349–358 (2001). https://doi.org/10.1080/02640410152006126

J. R. Kensrud and L. V. Smith, “In situ drag measurements of sports balls,” Procedia Eng. 2, 2437–2442 (2010). https://doi.org/10.1016/j.proeng.2010.04.012

J. R. Kensrud and L. V. Smith, “Drag and lift measurements of solid sports balls in still air,” Proc. Inst. Mech. Eng. Part P: J. Sports Eng. Technol. 232, 255–263 (2017). https://doi.org/10.1177/1754337117740749

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Story Collider – fighting for science at the frozen northern edge of Canada

A month ago I was a story teller at a Science Literacy Week event in Toronto called Story Collider. My story was about the excitement of travelling to the high Arctic for fieldwork the first time, only to find out during the first week that the government was cutting its funding. This prompted me down a path of science advocacy. This script aims to share some of my feelings on the experiences.

Story Collider was different from the other public speaking I’ve done. There was no one else on stage. There was nothing else on stage – no slides, no notes. Just me and a mic. The simplicity of this arrangement helped create a personal connection with the audience.

(Nice blog entry by science writer Mirjam Guesgen summarizing the event here.)

In this post I’ve added a few photos to illustrate what was in my head at the time. At some point, the audio recording of the event will be released and I’ll add a link.

Here we go…

Dan Weaver telling his story of fieldwork and science advocacy at Story Collider as part of Science Literacy Week
Dan Weaver telling his story of fieldwork and science advocacy at Story Collider in Toronto (photo credit: Ally Chadwick, @JustMyFreckles)

Flying across the Canadian Arctic is an exhilarating experience.

It’s a full day’s journey. Canada’s Arctic is huge. The landscapes are stunning; there are mountains and fjords, waterways and sea ice (for the moment anyway).

View from the plane to Eureka
View from the plane to Eureka

I do the trip when it’s the end of Polar Night, when light is returning after months of continuous darkness. In a small charter plane, the ride is loud and bumpy. There is no bathroom. With lots of scientific equipment along for the ride and everyone wearing massive parkas, space is limited. Every pound of weight is planned and verified. Weather can be difficult.

Inside the plane to Eureka
Inside the plane to Eureka (photo credit: Dan Weaver)

I remember the time the landing gear wheels got stuck – likely due to ice – and the landing in Resolute Bay (along the northwestern passages) was… abrupt. Another time, there were high winds. I remember trying to enjoy the landscape growing ever-closer out the window as the plane approached a runway at a steep angle – only levelling out at the last minute. It was a relief to land.

The effort is worth it. When I finally arrive in the middle of Ellesmere Island’s polar desert, it takes a half hour drive, down a desolate Arctic dirt road, to reach the Polar Environment Atmospheric Research Laboratory, or PEARL.

Remote Arctic road to the PEARL Ridge Lab
Remote Arctic road to the PEARL Ridge Lab (photo credit: Dan Weaver)

It’s further north than the northern lights, Inuit, and all Canadian settlements except the Alert military base. I have done the journey many times to do fieldwork.

Where is PEARL
Where is PEARL (Dan Weaver/Google Maps)

I’m an atmospheric physicist.

When everything is working well, I love going for hikes around the lab. Our parkas and snow pants mostly protect us from temperatures as low as -50ºC, but after a while your eyelashes end up freezing together. (The important thing is not to pull the ice off – melt it gently with your hands.)

Dan after a nighttime hike near Eureka
Dan after a nighttime hike near Eureka (photo credit: Dan Weaver/Paul Loewen)

If you can keep your eyelashes from freezing, it’s also awesome to see the wildlife. Arctic bunnies and foxes. (A few more photos here.) But sometimes, cables get chewed by curious Arctic wolves. So that’s a challenge, too.

Arctic Hare near PEARL
Arctic Hare near PEARL (photo credit: Dan Weaver)

Whether you’re a grad student or tenured professor, you’ll find yourself shovelling snow when the truck gets stuck in a snowdrift. I’ve shovelled snow next to the best in my field.

Shovelling snow between Eureka and the PEARL Ridge Lab
Shovelling snow between Eureka and the PEARL Ridge Lab (photo credit: Dan Weaver)

Without PEARL, scientists would have a big question mark across a significant part of the Arctic.

PEARL Ridge Lab
PEARL Ridge Lab (photo credit: Dan Weaver)

When I first joined the team, I was proud to be part of big, planet-wide endeavours aimed at understanding our changing world.

Installing instruments on the roof of the PEARL Ridge Lab
Installing instruments on the roof of the PEARL Ridge Lab at the start of the campaign (photo credit: Dan Weaver)

My first week at PEARL, in February 2012, was a whirlwind of activity. The cold was extreme, but I was thrilled. Maybe even moreso because of it. (I mean, I grew up in Ottawa, so I was ready for the Arctic, right??)

The Polar Vortex was overhead. The sawtooth mountain range carved out a jagged horizon to the east. A Canadian satellite mission flew overhead regularly; working in combination with PEARL instruments to observe the changing atmosphere. When I first arrived, the sun didn’t rise until 11 a.m. With each day, it rose a little bit earlier. After a month of being there, the sun set late into the evening.

Distant sawtooth mountains, viewed from the roof of the PEARL Ridge Lab
Distant sawtooth mountains, viewed from the roof of the PEARL Ridge Lab (photo credit: Dan Weaver)

When summer arrives, the sun doesn’t set at all.

sunset from the PEARL Ridge Lab
sunset from the PEARL Ridge Lab (photo credit: Dan Weaver)

….. But there was darkness on the horizon ….

A photo I’d taken of the lab and surrounding landscape during one of my very first days on the campaign made the front page of a major newspaper. I was excited but also heartbroken. The story was not about the tremendous science we were doing, but that it was all coming to an unexpected and sudden end. The government had decided to end funding for atmospheric and climate research. We would finish the campaign, and then the lab would be left in hibernation.

Le Devoir's coverage of the 2012 PEARL funding crisis
Le Devoir’s coverage of the 2012 PEARL funding crisis

A few weeks later, the last day of the campaign arrived. I made the most of it and enjoyed the view from the PEARL roof. I didn’t know if I’d ever return.

View from the PEARL Ridge Lab of Slidre Fiord
View from the PEARL Ridge Lab of Slidre Fiord (photo credit: Dan Weaver)

When I got back to Toronto, I realized PEARL’s closure was one story within a much larger one. Canada seemed to be dismantling its research capacity, with environmental work taking the biggest hit. The Experimental Lakes Area was closing, the census was cancelled, science libraries were being shut. Scientists in the federal government were fired by the thousands and those remaining were muzzled.

My perspective on the situation expanded beyond the PEARL facility, beyond the Arctic, and beyond science. Into politics. I started a #SavePEARL campaign.

Hmmm, I didn’t expect to get involved in politics when I decided to do a physics Ph.D… it’s not what I signed up for, but it was what was needed.

I wanted Canadians to understand what was being lost, and why it was important. I wanted there to be a public outcry to Save PEARL, and to save Canadian science.

Fast-forward a few years

I find myself marching down the streets of downtown Toronto, with a lab coat on and bullhorn in my hand. Hundreds of people march behind me.

I’m feeling exhilarated again. This time, not for doing science, but for rallying people to support it politically. Today, it still amazes me this was necessary at all.

I joined Canada’s leading group of science activists, who’d formed a new organization called Evidence for Democracy to advocate for science. There were marches and protests across Canada, calling on the government to fund science. It was a scene that would be repeated again on a global scale with the March for Science, which I also helped lead with a lab coat on and a bullhorn in my hand. This time, there are thousands of people behind me.

Dan kicks off the Toronto March for Science (credit: Paul Martin)
Dan kicks off the Toronto March for Science (photo credit: Paul Martin)

I learned that when Canadians speak loudly enough, politicians listen.

PEARL was eventually saved by new funding. There was a big gap in valuable long-term datasets that could never be recovered – the damage was done, but at least the work could begin again.

Walking to the PEARL Ridge Lab
Walking to the PEARL Ridge Lab (photo credit: Dan Weaver)

I returned to PEARL each winter for fieldwork, and operated instruments remotely during the rest of the year. I upgraded instrumentation, tested new measurement techniques, and have been using PEARL measurements to validate new satellite data. Busy filling in those question marks with data.

Dan adjusting beamsplitter door of the PEARL 125HR spectrometer
Dan adjusting beamsplitter door of the PEARL 125HR spectrometer (photo credit: Dan Weaver / Paul Loewen)

When the 2015 federal election arrived, I was pleased to see the winning party had lots of promises on science. I thought this time would be different. My years of campaigning for science were finally paying off.

Maybe Canadian research would be on firmer footing now.

Today, I’ve got what I need: cool photos, amazing memories, and a soon-to-be-finished Ph.D. But I know Canada still needs PEARL, if we’re to understand the Arctic and our atmosphere. Our international partners still need PEARL, so we can together fill in those many question marks about how our world is changing.

Dan meets Trudeau in Iqaluit
Dan meets Trudeau in Iqaluit and discusses need for long-term science funding. I tried!

I expected the new government would expand funding for atmospheric and climate science, but it didn’t. The only program supporting this type of work was ended. There have been no promises of funding in the future. I asked Trudeau himself when we, quite by chance, were both in Iqaluit several months ago. He said he’d talk to the Minister of Science. Nothing came of it.

PEARL is set to close. Again.

Will it be saved this time?

How many times will I have to put on a labcoat, and instead of walking into a lab, walk into the street to march for science?

Science only happens when we decide to support it.

Will you?

** Update: temporary short-term ‘bridge’ funding has been announced that ensure PEARL won’t close immediately. (CBC North story.). But it isn’t a long-term solution. It simply kicks the can down the road. (My thoughts here.) This script is as relevant as ever. Will I march for science again in 2019 to call on the government to fund PEARL? I hope it won’t be necessary.

Looking out at the high Arctic landscape
Looking out at the high Arctic landscape