explain xkcd - User contributions [en]

3181: Jumping Frog Radius

2025-12-16T07:29:48Z

Nachtvogel: Typo corrected (It's in fact "Schwarzschild" with a middle s.)

{{comic
| number = 3181
| date = December 15, 2025
| title = Jumping Frog Radius
| image = jumping_frog_radius_2x.png
| imagesize = 339x243px
| noexpand = true
| titletext = Earth's r_jf is approximately 1.5 light-days, leading to general relativity's successful prediction that all the frogs in the Solar System should be found collected on the surface of the Earth.
}}

==Explanation==
{{incomplete|This page was created by an CHAMPION PLANET-JUMPING FROG. Can someone calculate the size and mass of the largest object from which a champion frog can achieve escape velocity? Are there some named asteroids that are of sow low a mass that it would be possible for frog to jump of? (Of course there are some small ennough but do they have names)? Don't remove this notice too soon.}}
The {{w|Schwarzschild radius}} is essentially the size of a {{w|black hole}} -- the maximum distance from the center where gravity is so strong that light can't escape.

It is part of a solution to {{w|Einstein's field equations}}. It is usually calculated as the following:
:r = (2*G*M)/(c2),
where G is the {{w|gravitational constant}}, M is the mass of the object, and c is the {{w|speed of light}}.

If M is the mass of the {{w|Earth}} it would give the Schwarzschild radius for the Earth which is about 9 mm. (If all of Earth mass was pressed into a sphere of a bit less than 2 cm in diameter, it would become a black hole.)

The comic suggests a more useful radius. The ''Jumping Frog radius'', rjf, which is the size of a "planet" so that its gravity keeps a champion {{w|Frog jumping contest|jumping frog}} from being able to achieve {{w|escape velocity}}. Thus [[Randall]] has instead of c, the 299,792,458 m/s speed of light, used a much smaller value of 4.5 m/s, to represent the maximum speed of a jumping frog. It is possible that Randall got that value from [https://www.researchgate.net/publication/5661154_Explosive_Jumping_Extreme_Morphological_and_Physiological_Specializations_of_Australian_Rocket_Frogs_Litoria_nasuta this paper], which on page 179 puts an upper limit on the maximum velocity of adult {{w|Striped_rocket_frog|Australian rocket frogs}} at 4.52 m/s.
s
The title text points out that the rjf of the Earth is about 1.5 light days (compared to the 9 mm Schwarzschild radius), which is about 3 times the distance to {{w|Pluto}}. Since Earth's surface is much smaller than this{{cn}}, no frogs will be able to escape, so they'll all collect here on Earth. As far as we know, all the frogs in the Solar System are on Earth, so the data apparently matches the theory.

==Transcript==
:[The panel shows a large formula to the left and a small drawing to the right. The formuals right side is drawn above and below the division line:]
:rjf = 2GM/(4.5m/s)2

:[The drawing to the left shows a very small planet with the radius indicated with a labeled dotted arrow pointing from the center straight up. A frog is shown jumping on the surface. This is indicated with a parabolic dotted line going from a frog sitting on the surface near the top of the planet, up to the frog shown soaring through the air with its limbs stretched out about as high above the surface as the planet's radius. At this point the frog is making a sound. Then the dotted line goes down to about a quarter of the way around the planet where the frog lands making a noise.]
:Arrow label: rjf
:Frog: Ribbit
:Landing: Plop

:[Caption below the panel:]
:More practically useful than the Schwartzchild radius, the '''''Jumping Frog Radius''''' is the radius at which an object's gravitational pull is so strong that even a champion jumping frog can't escape.

{{comic discussion}}<noinclude>
[[Category:Physics]]
[[Category:Astronomy]]
[[Category:Animals]]

3097: Bridge Types

2025-06-05T07:05:28Z

Nachtvogel: /* Explanation */

{{comic
| number = 3097
| date = June 2, 2025
| title = Bridge Types
| image = bridge_types_2x.png
| imagesize = 740x581px
| noexpand = true
| titletext = Pontoon bridges are just linear open-sided waterbeds.
}}

==Explanation==
{{incomplete|This page was recently created by a TESSERACT BRIDGE ABUTMENT. Don't remove this notice too soon.}}
This comic shows, in a four-by-four grid of images, a series of bridge types. The first two rows of images are of authentic bridge types, whereas those in the last two rows are progressively more absurd, although real-life examples of some of them exist, as shown in the table below. The joke lies in the progression of bridge types from the simple and straightforward to the complex and ridiculous.

{| class="wikitable"
!Label
!style="width:7em;"|Status
!Type
!Notes
|-
|Plank
|Real
|{{w|Beam bridge}}
|A straightforward piece of solid material (in this case, made of solid wood, but there are {{w|Clapper bridge|other materials}}) is the most basic form of bridge, and generally the easiest to construct, but also the weakest. Consequently, such bridges are only suitable for small spans and light weights (such as a footbridge over a stream).
|-
|Rope
|Real
|{{w|Simple suspension bridge}}
|Rope bridges consist of several lengths of rope anchored on both sides of the span. Typically, one or more ropes will be intended to support the crossing load (possibly with boards or some other walkway between them), and additional ropes will act as handrails, reducing the risk of falling. These are typically only intended for foot traffic, due to their light construction and lack of rigidity. Because of the simple materials and relative ease of construction, they're often used as improvised bridges.
|-
|Truss
|Real
|{{w|Truss bridge}}
|A truss is a common type of framework consisting of supports connected in a series of triangles which provide support for a load. This design provides significant strength and rigidity with minimal material and weight. A truss bridge can either have the truss above the bridge platform (as in the drawing) or underneath it (also known as a deck truss). This is the first bridge type on this list which is commonly used for vehicle traffic.
|-
|Trestle
|Real
|{{w|Trestle bridge}}
|A trestle bridge is held up by supports reaching all the way to the ground beneath. Typically at least some of the supports will slope outward to give a larger base of support. Once common for railroads, these are less popular nowadays, but are still seen in certain areas and applications.
|-
|Arch
|Real
|{{w|Arch bridge}}
|Arches are one of the oldest kinds of bridges for carrying significant loads. They can be made out of rock or metal. Each span consists of an arch resting on supports. Simple arch bridges rest on both sides of a river or other gap, but longer bridges (as in the drawing) will have intermediate pillars to support multiple arches. The arches distribute the load, allowing a relatively small number of pillar to support weight across the entire deck of the bridge.
|-
|Suspended Arch
|Real
|{{w|Through-arch bridge}}, possibly {{w|Tied-arch bridge}}
|A through arch bridge uses a similar concept as an arch bridge, but the deck is entirely or partially suspended below the top of the arch (in this case fully suspended, at the bottom of the arch). The tie of a tied arch bridge refers to using the deck as a tension member to restrain the horizontal spreading of the arch; without a tie, the arch's foundation must resist that horizontal loading. From the picture, it is not clear whether the deck is acting as a tie. Such bridges may use a single arch (as in the drawing) or multiple arches in succession.
|-
|Draw
|Real
|Drawbridge (more precisely a fixed-trunnion {{w|Bascule_bridge|bascule bridge}})
|Drawbridges are used to allow ships to pass through obstacles like bridges. They use various methods to raise one or multiple sections of the bridge to create enough height clearance for vessels to pass through, in this case using a cable to rotate the bridge about a pivot point (trunnion).
|-
|Suspension
|Real
|{{w|Suspension bridge}}
|A suspension bridge suspends its deck with cables or rods from a cable linked to a pillar and a point a certain distance from each pillar
|-
|Filler
|Real method of maintaining {{w|Grade (slope)|grade}}, not really a 'bridge'
|{{w|Embankment (earthworks)|Embankment}}, {{w|Causeway}} or even a {{w|Dam}}
|Serves the purpose of allowing travel across the gap, but by removing (or {{w|Culvert|mostly removing}}) passage through the gap itself. By filling the gap with hard, irregular material (most commonly rocks), support can be provided, while still allowing water to flow through the gaps. Due to the generally small size of the gaps, generally only slow-flowing water can reliably get through.
|-
|Budget Overrun
|Real (with an absurd name)
|{{w|Cable-stayed bridge}}
|Specifically, the pictured bridge is a {{w|cantilever spar cable-stayed bridge}}, similar in appearance to the {{w|Samuel Beckett Bridge}} in Dublin or the {{w|Erasmusbrug}} in Rotterdam. Many bridges in this category suffer severe cost overruns. Randall may be drawing upon his local knowledge of the {{w|Leonard P. Zakim Bunker Hill Memorial Bridge|Zakim Bridge}} in downtown Boston's {{w|Big Dig}}, also strongly associated with cost overruns.
|-
|Jump
|Not real
|Similar to a pair of small {{w|cantilever bridge}}s, constructed at an incline.
|A "bridge" that appear to be being used by a skateboarder, though in a manner far more dangerous than any jump in a typical skatepark. While not {{w|London Buses route 78#History|normally}} a feature of the highway, jump ramps can be used for gap-crossing stunts by almost any vehicle with sufficient speed. Partial bridges, which allow ''some'' vehicles using them to safely cross the gap, iconincally featured in {{w|The Dukes of Hazzard}} TV show, as well as common in various {{w|The Man with the Golden Gun (film)#Car stunts|action}} {{w|Speed (1994 film)#Filming|films}}, though typically less easy to use correctly than the setting implies.
|-
|Halfhearted
|Not real under this name, but with real analogs
|[https://www.archdaily.com/184921/moses-bridge-road-architecten Moses bridge]
|The diagram shows that there was barely any attempt to bridge the gap in the landscape at all, just take the 'deck' down into it and back up out again. The concept may have been inspired, in part, by [https://www.fastcompany.com/90186315/the-strange-art-of-the-melting-bridges-of-google-earth an artifact in Google Earth software].
Structures exist, at the {{w|Fort de Roovere}} in Halsteren, Netherlands and elsewhere, that resemble this 'solution', though these would have involved much thought and commitment in their building, possibly more 'hearted', even, than any more conventional bridge design, especially in the provision of stairs to allow easier ingress/egress (at least for foot traffic) than in the comic's version.
|-
|Waterbed
|Not a bridge
|{{w|Waterbed}}
|Rather than a bridge, it is more like another version of a causeway (see 'Filler') using trapped water to maintain the upper surface.
Named for a 'mattress' type, which is usually a raised surface ''on top of'' a piece of bedframe, with an unusual approach to padding and comfort.
|-
|L'Engle
|Not real
|[https://www.refinery29.com/en-us/2018/03/192728/tesseract-definition-wrinkle-in-time-space-dimension Tesseract AWIT] not {{w|Tesseract|Tesseract (geometry)}}
|References {{w|A Wrinkle In Time}} by Madeleine L'Engle. Characters cross great distances by "tessering", moving via a tesseract through a higher dimension which essentially brings the two ends of the journey together from the perspective of the traveler. The image shows the two ends of the gap being brought together, with the gap apparently crumpled in between them.
|-
|Fun
|Not real
|{{w|Vertical loop}}
|It is a loop-de-loop, not normally a practical or necessary way of bridging a gap. Something previously seen, in an arguably even more imprctical manner, in [[2935: Ocean Loop]].
|-
|Repurposed Elevator
|Real, but not as displayed
|Horizontal elevator / {{w|People mover|People mover}}
|There are various implementations of such designs, the best-known one is probably the {{w|Schmid Peoplemover|Schmid Peoplemover}}.
However, unlike a regular people mover, where the door stays upright, the image shows a regular elevator that has been rotated 90 degrees.
|-
|''(Title text)''
|Real
|{{w|Pontoon bridge}}
|Pontoon bridges are described as a series of fictitious "waterbed bridges", as shown above, but constructed without sides. This would mean that that the 'bed'-supporting water flows in one side and out the other, if there is any passage or tidal flow of water. It may technically mean that you cannot cross {{w|The Same River Twice|the same bridge twice}}.
Pontoons rely upon buoyancy, either of the whole deck or distinct floating elements, whereas an enclosed "waterbed" bridge would rely upon the strength of the membrane to keep the mass of water within it, and thus the deck above that mass.
|}

==Transcript==
{{incomplete transcript|Don't remove this notice too soon.}}
:Bridge Types

:[A 4x4 matrix of 16 ways to cross the same rectangular hole in the ground]

:Plank [shows a plank laid over the hole]

:Rope [shows a rope bridge with rope guardrail]

:Truss [shows a truss bridge with a triangular truss above the bridge deck]

:Trestle [shows a trestle bridge]

:Arch [shows stone arches supporting a straight deck]

:Suspended Arch [shows a single arch, with the bridge deck suspended from it]

:Draw [shows a truss bridge, with one half opened like an unrealistic draw bridge]

:Suspension [shows the bridge deck suspended from a cable strung between two pillars and the shores]

:Filler [shows the hole filled with dirt and stones]

:Budget Overrun [shows a bridge deck suspended by cables from an artistically shaped pillar]

:Jump [shows two ramps at the edges of the hole, and a skateboarder jumping across the hole]

:Halfhearted [shows a ramp at each side of the hole that leads down to the bottom]

:Waterbed [shows the hole filled with water, two fish and an octopus, a wobbly covering, and two stick figures crossing]

:L'Engle [shows the hole warped such that the opposite shores meet]

:Fun [shows a loop-de-loop rollercoaster bridging the hole, and a skateboarder using it to get across]

:Repurposed Elevator [shows an elevator tower, rotated sideways as a whole, laid across the hole. 2 stick figures using the elevator are also rotated.]

{{comic discussion}}<noinclude>

[[Category:Engineering]]
[[Category:Comics featuring Cueball]]
[[Category:Multiple Cueballs]]
[[Category:Animals]]

Talk:3097: Bridge Types

2025-06-03T06:00:44Z

Nachtvogel:

For budget overrun, see olympic stadium of Montreal, Quebec, Canada.

[[Special:Contributions/162.158.126.202|162.158.126.202]] 01:23, 3 June 2025 (UTC)

Very disappointed there's no bridge card game reference, but I guess that's not one of Randall's types of nerdiness :( [[Special:Contributions/172.71.254.203|172.71.254.203]] 01:45, 3 June 2025 (UTC)

I would like to note that cable stayed bridges, budget overrun here, are much cheaper than equivalent suspension bridges. It because they use less materials and can be built faster meaning less labor. [[Special:Contributions/172.69.58.51|172.69.58.51]] 01:50, 3 June 2025‎
:Tru dat in general, but I think that this is a reference to the {{w|Leonard_P._Zakim_Bunker_Hill_Memorial_Bridge|Zakim Bridge}} in downtown Boston, part of the {{w|Big_Dig|"Big Dig"}} project that became notorious for its budget overruns and related shenanigans. Given that Randall M. lives in Boston, that makes this panel something of an inside joke. [[Special:Contributions/172.71.147.224|172.71.147.224]] 03:15, 3 June 2025 (UTC)

The [[wikipedia:St. Louis Arch|St. Louis Arch]] is a repurposed-elevator-suspended-arch-but-without-the-base-and-wires bridge if you squint hard enough. The elevator is also fun. [[Special:Contributions/172.69.67.214|172.69.67.214]] 01:57, 3 June 2025 (UTC)

Nothing about a a [[wikipedia:Bridge circuit|bridge circuit]] or these [[Wikipedia:Bridges (disambiguation)|many]] [[wikipedia:other|other]] bridges either. Sigh. [[Special:Contributions/172.69.67.214|172.69.67.214]] 01:57, 3 June 2025 (UTC)
:And where, oh where, are Lloyd, Beau, Jeff, and Jordan? [[Special:Contributions/162.158.41.84|162.158.41.84]] 03:19, 3 June 2025 (UTC)

The L'Engle is a take off on a Wrinkle in time? But this one is in space? -- [[User:162.158.91.124|162.158.91.124]] ([[User talk:162.158.91.124|talk]]) 02:26, 3 June 2025‎ ''(please sign your comments with <nowiki>~~</nowiki>~~)''
:There's some space-warping in L'Engle's books. [[Special:Contributions/162.158.174.63|162.158.174.63]] 02:44, 3 June 2025 (UTC)

The "budget overrun" bridge doesn't really look like the Zakim bridge to me. It looks a lot like the Samuel Beckett Bridge in Dublin. I don't know what the budget of that bridge was, but according to wiki it cost 60 million euros, which sounds like a lot given that the bridge isn't all that long or wide. [[Special:Contributions/172.70.126.87|172.70.126.87]] 03:24, 3 June 2025 (UTC)
: Perhaps if Randall M. drew too close a likeness to the Zakim Bridge, he feared a visit from officials with lawyers and/or cement shoes. ("Only the paranoid survive ...") It seems, from a quick tour of the Internet, that words like "grandiose and overblown" are easily applied to cable-stayed bridge designs/aesthetics. I wasn't easily able to find information on budget overruns for these bridges, and see the commentator above who pointed out the lower costs overall of cable-stayed ''vs'' suspension bridges. But as a former resident of Greater Boston, I can report the pervasiveness of the Big Dig and its challenges, budgetary and otherwise, in local life and lore. [[Special:Contributions/172.68.22.108|172.68.22.108]] 04:32, 3 June 2025 (UTC)
::The cable-stayed bridge is the current darling of artists that accidentally went to engineering school, who are notorious for running over budget and behind schedule. [[User:RegularSizedGuy|RegularSizedGuy]] ([[User talk:RegularSizedGuy|talk]]) 04:40, 3 June 2025 (UTC)
: I can see the suggestion of the Beckett bridge, but in my eyes the obvious template would be [https://en.wikipedia.org/wiki/Erasmusbrug Rotterdam's Erasmus Bridge] [[User:Nachtvogel|Nachtvogel]] ([[User talk:Nachtvogel|talk]]) 06:00, 3 June 2025 (UTC)

I think the repurposed elevator should be considered a dig at Elon Musks The Boring Company, even though they tunnel rather then bridge
[[Special:Contributions/162.158.182.138|162.158.182.138]] 04:37, 3 June 2025 (UTC)

2968: University Age

2024-08-06T09:12:56Z

Nachtvogel: /* Explanation */

{{comic
| number = 2968
| date = August 5, 2024
| title = University Age
| image = university_age_2x.png
| imagesize = 317x388px
| noexpand = true
| titletext = This only makes it more urgent that we adopt my roadmap for the next 10 years, which should put us solidly in the lead.
}}

==Explanation==
[[Cueball]] has been the leader of a university for the last five years. In a speech, he declares that his goal during those five years has been to make his university overtake the age of the oldest university of his state, which was then two years older than his own (215 years vs 213 years old). He declares that an intensive program he funded he has managed to make his university five years older, making it three years older than the other university was when he took the role. Due to the laws of time, this would have happened anyway, whatever he had done, or if he'd done nothing at all (barring his leadership being so catastrophic that the University ceased operating).

The final line of Cueball's speech, "Unfortunately, I have terrible news," presumably precedes the announcement that the rival university has also aged 5 years and is therefore just as far ahead as they were before (as it will forever be, until Cueball manages to put the rival university on a spaceship and send it on a journey at an appreciable fraction of the speed of light, whereby time dilation will allow his university to catch up, or alternatively, finds a way to travel back in time to establish the university a few years earlier; he might as well think of a way of taking the relation of the ages of the universities as measure (223/225 is closer to 1 than 213/215) and thus they're "racing up" towards the older rival, although never be able to catch up).

In the title text, the "roadmap for the next 10 years" implies more of the same ineffective efforts, or perhaps strategies to undermine the rival.

==Transcript==
:[Cueball is standing behind a lectern on a stage. He has raised a finger in the air while addressing an unseen audience.]
:Cueball: When I took the helm five years ago, our university was 213 years old – the second oldest in the state, just behind our 215 year old rival.
:Cueball: Under my leadership, we've funded an intensive program to increase our age to 218, overtaking our rival by 3.
:Cueball: Unfortunately, I have terrible news.

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Public speaking]]
[[Category:Time]]

2968: University Age

2024-08-06T09:11:21Z

Nachtvogel: /* Explanation */

{{comic
| number = 2968
| date = August 5, 2024
| title = University Age
| image = university_age_2x.png
| imagesize = 317x388px
| noexpand = true
| titletext = This only makes it more urgent that we adopt my roadmap for the next 10 years, which should put us solidly in the lead.
}}

==Explanation==
[[Cueball]] has been the leader of a university for the last five years. In a speech, he declares that his goal during those five years has been to make his university overtake the age of the oldest university of his state, which was then two years older than his own (215 years vs 213 years old). He declares that an intensive program he funded he has managed to make his university five years older, making it three years older than the other university was when he took the role. Due to the laws of time, this would have happened anyway, whatever he had done, or if he'd done nothing at all (barring his leadership being so catastrophic that the University ceased operating).

The final line of Cueball's speech, "Unfortunately, I have terrible news," presumably precedes the announcement that the rival university has also aged 5 years and is therefore just as far ahead as they were before (as it will forever be, until Cueball manages to put the rival university on a spaceship and send it on a journey at an appreciable fraction of the speed of light, whereby time dilation will allow his university to catch up, or alternatively, finds a way to travel back in time to establish the university a few years earlier; also a way of taking the relation of the ages of the universities as measure (223/225 is closer to 1 than 213/215) and thus they're "racing up" towards the older contestant, although never catching up).

In the title text, the "roadmap for the next 10 years" implies more of the same ineffective efforts, or perhaps strategies to undermine the rival.

==Transcript==
:[Cueball is standing behind a lectern on a stage. He has raised a finger in the air while addressing an unseen audience.]
:Cueball: When I took the helm five years ago, our university was 213 years old – the second oldest in the state, just behind our 215 year old rival.
:Cueball: Under my leadership, we've funded an intensive program to increase our age to 218, overtaking our rival by 3.
:Cueball: Unfortunately, I have terrible news.

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Public speaking]]
[[Category:Time]]