#dihedral angles

[er-cryptid]

[july-19th-club]

just remembered that when i first got really into turkey vultures i learned about airplanes bc i had to go look up 'dihedral' because the turkey vulture is one of the best soaring birds we have in my area and it's because of not just their wing shape, which is both more tapered toward the tips AND more spread out, excellent for taking advantage of wind currents and, say it with me everyone, thermals but because of their dihedral, which is the upward angle at which the wings sit, which allows them to soar without expending much energy for such long periods of time anway i quickly forgot all about how dihedral works on airplanes because i was too busy with my best friend cathartes aura aura anyway who wants to talk abt the noble turkey buzzard im simply dying to talk abt the noble turkey buzzard

[some-teeth-in-a-trench-coat]

Is there a way to derive the dihedral angle of a regular polyhedron using only the Schläfli symbol without just looking it up how do you figure out anything about a spherical regular polygon with n vertices without knowing the angles only the sides am I just trying to do the impossible or are the articles I find just misleadingly short

[iwannakissasopwithcamel]

Ritter Model S ‘Fink’ - "Astrid Ritter's Magnum Opus"

Role: Scout Served With: Macchi Republics First Flight: 1597 Strengths: Supreme Dogfighter Weaknesses: Unstable, Overspeed Inspiration: Sopwith Snipe (1918) Backer: Tom

Description:

The last Ritter rotary, the Model S consumed nearly half a decade of the designer’s life in perfecting it. A redesign of the Model F, improved in every way, the Model S carries the frightening W.O.3 230 horsepower engine. Both wings had to be given dihedral angles to compensate for the immense torque.

The Fink had aggressive turn characteristics, robust construction, and could outrun anything that could outturn it. Though they never completely replaced the Model F, it was soon known and feared by its enemies, and it was the last, best chance for the doomed Macchi Republics.

Though rare, many dogfight aces consider them to be the best rotary biplanes in the world. Few survived, most of them cut apart for the engines after Macchi surrendered, so each one is treasured

[hidden-but]

when you're trying to understand the reasoning behind dihedral angles

[abalidoth]

blanket idea:

If you fit four regular pentagons around a vertex, they buckle in such a way that their dihedral angle is pretty close (but not exactly) the dihedral angle of a dodecahedron. Fabric is squishy enough to make that work; if you continue the pattern, you can make a tiling that's topologically the Cairo tiling but made of regular (granny) pentagons. It'll be flat in the long run but kinda egg cartoned locally.

The Cairo tiling has four translation classes of pentagon, so you can use four different yarns. If you start from each pentagon's short edge and count two more edges clockwise, you single-cover every long edge and double cover every short edge. You can use this to stitch together the blanket just from the tails of the granny pentagons, with no extra yarn!

[xaeorian]

Did steam break you?

Was aerodynamics too much?

fuckkkk maybe. i haven’t done any of it

we just sat in class and discussed university so i just couldn’t write anything. i did draw a dihedral angled wing though.

[aviationschool]

✈️ Understanding Stability: Dihedral vs. Anhedral Wings 🛫

Ever wondered why airplane wings are angled differently? ✈️ Dihedral wings (upward angle) enhance stability, keeping the plane level by naturally correcting roll. 🛫 Anhedral wings (downward angle) boost maneuverability, ideal for fighter jets and acrobatic planes. Knowing the difference helps us appreciate the design choices behind different aircraft. 🌐 https://www.youtube.com/shorts/N0jZS-14nQQ #Aviation #AircraftDesign #Dihedral #Anhedral #AviationGeeks

[slimeslam]

Summary: Halonen et al. (2019)

In this post I will summarize the article by Halonen, R., Zapadinsky, E, Kurtén, T. and Vehkamäki, H. (2019). Rate enhancement in collisions of sulfuric acid molecules due to long-range intermolecular forces. Atmospheric Chemistry and Physics, 19, 13355–13366.

The contribution of new particle formation by the clustering of molecules in the atmosphere is one of the key uncertainties in climate modelling. Traditionally new particle formation is modelled by kinetic gas theory which fails to take into account the long-range interactions between the atmospheric particles. Thus the formation rates of atmospheric particles are generally underestimated. The work by Halonen et al. studies the collisions between sulfuric acid molecules using computational techniques.

The intermolecular interactions in the simulations are described by short-range Lennard-Jones interactions between the single atoms and and long-range Coulomb interactions between the partial charges of the molecules. Intramolecular interactions are described in different models on one hand by simple harmonic spring forces between the atoms and on the other hand taking into account the vibration of bond angles and dihedral angles (torsion angles). Even though the former simpler model performed slightly better predicting the structures of the dimers (two molecules bound together), the latter model is chosen in this work as it predicts the intramolecular vibrations better. Intramolecular vibrations are important when studying molecular collisions. Also it is noted that the latter model is more portable for future research.

The collision simulation was performed under the assumption that the two molecules don't interact with surrounding air, which is deemed reasonable as the collisions between sulfuric acid molecules happen considerably faster than the collisions between other molecules. Over 500 thousand simulations were performed using different starting configurations for the molecules.

Classically the collision rates are calculated assuming that the binding of two molecules is certain if the molecules are able to surmount the centrifugal effective energy barrier present in a two-particle central field model. From this an analytical presentation for the impact parameter (how far from each other the molecules can pass each other as a function of their relative velocity) can be derived. Finding the average interaction energy of the particles from the simulations is needed for calculation fo the parameter, which in turn is needed for the calculation of collision rates.

The results from the simulations are found to correspond to the analytical model quite well. With a shorter impact parameter and lower relative velocity the collision probability is found to approach one as is expected. However, even if a collision happens, at high velocities a dissociation of molecules shortly after is possible as the molecular bonds receive a high amount of kinetic energy. In smallest velocities the collision probability is found to be reduced as well, as the intermolecular repulsive interactions can sometimes exceed the kinetic energies. The collision rate was found to be enhanced by the factor of 2.2 with respect to the kinetic gas theory modle.

Halonen et al. conclude that their force field model of choice was able to describe the structure and vibrations of the dimers. The impact parameters and collision rates were found to be significantly lager compared to kinetic gas theory. This is consistent with the difference between observed and kinetic gas theory results. The authors state that these techniques can applied for similar future simulations as well, however, in order to correctly model atmospheric processes, all the collisions between molecular clusters of different sizes must be studied. For this reason there is a need for more coarse-grained approaches.

Selected glossary:

collision cross-section - vaikutusala; The effective cross-sectional area of the molecules in the collision. In kinetic gas theory the molecules are modelled as hard spheres, in which case the collision cross-section is simply the cross-sectional area of the sphere. In reality for many gases area is considerably larger due to intermolecular interactions.

impact parameter - vaikutusalan säde; The radius of the effective cross-sectional area, how far away the particles moving with a certain relative velocity can maximally be from each other for the collision to happen.

collision rate coefficient - törmäystaajuus; The rate of collisions of certain gas species with certain concentrations and collision cross-sections.

central field model - keskeiskenttämalli; The assumption that the forces of particles due to one another are radial, in which case their movement is essentially described by a one-dimensional equation of motion.

centrifugal barrier - keskipakoisvoimaan liittyvä energiavalli; An effective potential energy barrier arising in the central field model. Analogous to orbits of heavenly bodies: they are hindered from colliding due to this effective barrier.

potential of mean force - keskivoiman potentiaali; The expectation value of the interaction potential of the two particles as a function of intermolecular distance.

ALMS progress: reading 1 h 10 min, text 1 h 40 min, total 2 h 50 min

37 h 45 min

[ettolrach-uwu]

I really hate it when people ask for "real life applications" because often times it's asked as a way to prove that what maths is being done is irrelevant. I always remember Matt Parker saying in one of his comedy shows, "even the Natural numbers aren't that real, you won't find a number line in the wild."

I think that at a certain point, probably after ℕ ∪ 0, it's impossible to think of a good "real life" example for maths concepts. Negative numbers are explained as floors of a building, with ground floor being 0, the basement being -1, second basement being -2, etc. But you don't need negatives for this, there are many buildings where the ground floor is actually -1, maybe because technically the building is built on a gradient and the 0th floor is "ground level" at a different entrance even after the main entrance changed to the -1st level. Or debt, you can talk about debt entirely using "credit" and "debit", in fact, my gas and electricity bills are entirely in those words without the use of negative numbers.

Thus, I think we need to give examples of these concepts not by trying to link them to some real world "thing", but by telling about applications of that thing.

So for complex numbers, instead of trying come up with a real world thing which corresponds to it, why not talk about trisecting an angle, or my personal favourite example, solving the cubic/the cassus irreducibilis that arises when you try to solve one. It is a lot easier to explain why we need to do either of those (solving cubics is helpful in physics, linear algebra solves cubics all the time) then to try to think of examples of this what "are" complex numbers.

Similarly, this continues on to even more abstract concepts. Group theory has one of my favourite examples that I found on YouTube recently: the dihedral group of order 10, can be used for (base 10) checksums with credit card numbers. Category theory has concepts which are used in computing (monads).

This way, I feel like students can get an understanding of why they're learning things and how they were discovered, if those are used as an example (integral calculus is great for this).

Okay this is going to be a bit more venty than usual but I've seen a post about complex numbers that's annoyed me.

The only reason you are less willing to accept the existence of imaginary numbers is you aren't taught it in a way that helps build intuition nor from as young an age.

Complex numbers have been around for centuries. They aren't some new fangled thing that are mysterious to mathematicians. Part of the non-mathematician's conception of imaginary numbers certainly isn't helped by their name but I have to say I think the internet and clickbait are a lot to blame for that too.

A lot of mathematics is invented by thinking "what if..." and rolling with it to see if you can draw anything meaningful from it. "What if numbers less than 0 exist?", well then you have given meaning to something like 2-7. "What if we could divide any two integers?", now you can talk about what 3/7 means. Asking "what if square roots of negative numbers did exist?" let's us explore whether √(-1) would give us something with consistent and useful properties and it turns out it does (technically we just declare i²=-1 and i=-√(-1) does everything just as well).

"You can't take the square root of a negative number" is drilled into pupils heads at school when really the message should be a more subtle "there aren't any real numbers that are the square root of a negative number". It's a subtle but important difference. It's exactly like saying "there aren't any natural numbers x such that for naturals numbers y and z with z>y we have x=y-z". You'd be pretty hard pressed to find anyone saying that the latter is impossible.

I don't really know how to end this. I'm just frustrated

[wiackcom]

Fisker's head-turning new flagship Ronin ushers in a bold styling direction for the brand. As their exhilarating electric halo model, it blends lavish grand touring appointments with extreme performance capabilities. Fisker's Past and Future Stylistic Vision Fisker has crafted gorgeous vehicles like the Tramonto and Karma in the past. The Ronin points to an exciting design path for upcoming models. Founder's Strong Design Experience Henrik Fisker honed his skills at BMW, Aston Martin and his own coachbuilding company before founding Fisker. Signature Styling Cues The unified front lightbar with split LED accents will define Fisker vehicles moving forward. Diverse Model Range Fisker will offer mainstream and luxury models ranging from the Ocean SUV to the Ronin sports car. Seductive Exterior Styling The Ronin's dramatic sports car proportions make an unforgettable visual statement. Elongated Hood In classic grand tourer fashion, the Ronin has an extensive hood stretching forward. Truncated Rear Deck The shortened rear deck accentuates the cab-forward design. Innovative Dihedral Doors Distinctive rear-hinged rear doors ease access to the 2+2 cabin configuration. Retractable Hardtop A folding carbon fiber roof panel enables open-air motoring on demand. Arresting Presence The Ronin's styling projects attitude and athleticism from every angle imaginable. Bespoke Interior Design Inside, the Ronin focuses on driver engagement while coddling passengers. Roomy Layout Two rows of seats coddle four adults in absolute comfort. Opulent Materials Expect decadent leather, aluminum and carbon fiber trimmings throughout the cabin. Advanced Technology Fisker's signature rotating central screen will likely make an appearance. Generous Cargo Space The rear trunk will easily swallow luggage for extended grand touring getaways. Extreme Performance Powertrain Specs With 1000 horsepower available, the Ronin promises exotic car acceleration. Triple Electric Motor AWD Three electric motors enable precise torque vectoring and instant acceleration. Warp Speed Acceleration Few vehicles can match the Ronin's sub-2-second 0-60 mph sprint time. Unbridled Top Speed Expect a top speed well above 200 mph for unrestrained high-speed road tripping. Repeated Performance Sophisticated cooling maintains the powertrain's output during hard driving. Revolutionary Battery Tech and Range The Ronin's 600 mile range target surpasses any current production EV's range. Structure-Integrated Battery Supplementary batteries within the chassis add range beyond the underfloor battery pack. Target Max Range Fisker estimates around a 600 mile maximum range for the production version. Ultra Fast Recharging With 350kW charging, brief 15-20 minute stops will restore substantial range. True Long-Distance GT Ability The immense range capacity enables authentic long-haul electric grand touring. Dynamic and Engaging Driving Experience The Ronin's tailored chassis promises exciting performance reflecting the exterior design. Dialed-in Suspension Tuning Expect the chassis and suspension to be optimized for sharper reflexes and handling. Massive Brakes Giant brake discs and calipers supply fade-free stopping power. High-Performance Rubber Bespoke ultra-high-grip tires connect the prodigious power to the road. Driver-Focused Setup The steering, suspension and brakes aim squarely at an intense, rewarding driving experience. Cruising Comfort A more pliant suspension mode maintains composed comfort when desired. Target Customers and Competitive Set Well-to-do driving fans comprise the target demographic for Fisker's opulent new halo model. Luxury EV GT Segment The Ronin competes among upcoming luxury electric grand touring convertibles. Key Rival Automakers Polestar, Genesis and Tesla all aim for the same affluent consumer base.

Tech-Savvy Early Adopters Wealthy technophiles will be drawn to the carbon-conscious yet extravagant sports car. Brand Cachet Fisker must elevate its brand prestige to match established luxury marques. Expected Pricing and Availability The 2026 Ronin will command a substantial sum consistent with its positioning and exclusivity. Production Timing Manufacturing should start in late 2025 for the 2026 model year. Base MSRP Pricing initiates at $385,000 before options or delivery charges. Reservations Open Now Fisker welcomes $2000 deposits to reserve build slots immediately. Ultra-Limited Numbers Strictly capped annual production will maintain the Ronin's elite status. FAQs What is the Ronin's body style? It's a 2-door coupe with rear-hinged rear doors for easier cabin entry and exit. What range can it drive on one charge? Fisker targets approximately 600 miles between charging stops. How quick is the Ronin? With 1000 horsepower, 0-60 mph happens in around 2 seconds. Top speed exceeds 200 mph. Does the roof retract? Yes, the carbon fiber roof panel folds away to allow open-air driving. When can I purchase the Ronin? Production commences in late 2025, with initial deliveries in 2026. Reservations are already open. #Wiack #Car #CarInsurance #CarRental #CarPrice #AutoLoans

[sportyconnect]

Fisker's head-turning new flagship Ronin ushers in a bold styling direction for the brand. As their exhilarating electric halo model, it blends lavish grand touring appointments with extreme performance capabilities. Fisker's Past and Future Stylistic Vision Fisker has crafted gorgeous vehicles like the Tramonto and Karma in the past. The Ronin points to an exciting design path for upcoming models. Founder's Strong Design Experience Henrik Fisker honed his skills at BMW, Aston Martin and his own coachbuilding company before founding Fisker. Signature Styling Cues The unified front lightbar with split LED accents will define Fisker vehicles moving forward. Diverse Model Range Fisker will offer mainstream and luxury models ranging from the Ocean SUV to the Ronin sports car. Seductive Exterior Styling The Ronin's dramatic sports car proportions make an unforgettable visual statement. Elongated Hood In classic grand tourer fashion, the Ronin has an extensive hood stretching forward. Truncated Rear Deck The shortened rear deck accentuates the cab-forward design. Innovative Dihedral Doors Distinctive rear-hinged rear doors ease access to the 2+2 cabin configuration. Retractable Hardtop A folding carbon fiber roof panel enables open-air motoring on demand. Arresting Presence The Ronin's styling projects attitude and athleticism from every angle imaginable. Bespoke Interior Design Inside, the Ronin focuses on driver engagement while coddling passengers. Roomy Layout Two rows of seats coddle four adults in absolute comfort. Opulent Materials Expect decadent leather, aluminum and carbon fiber trimmings throughout the cabin. Advanced Technology Fisker's signature rotating central screen will likely make an appearance. Generous Cargo Space The rear trunk will easily swallow luggage for extended grand touring getaways. Extreme Performance Powertrain Specs With 1000 horsepower available, the Ronin promises exotic car acceleration. Triple Electric Motor AWD Three electric motors enable precise torque vectoring and instant acceleration. Warp Speed Acceleration Few vehicles can match the Ronin's sub-2-second 0-60 mph sprint time. Unbridled Top Speed Expect a top speed well above 200 mph for unrestrained high-speed road tripping. Repeated Performance Sophisticated cooling maintains the powertrain's output during hard driving. Revolutionary Battery Tech and Range The Ronin's 600 mile range target surpasses any current production EV's range. Structure-Integrated Battery Supplementary batteries within the chassis add range beyond the underfloor battery pack. Target Max Range Fisker estimates around a 600 mile maximum range for the production version. Ultra Fast Recharging With 350kW charging, brief 15-20 minute stops will restore substantial range. True Long-Distance GT Ability The immense range capacity enables authentic long-haul electric grand touring. Dynamic and Engaging Driving Experience The Ronin's tailored chassis promises exciting performance reflecting the exterior design. Dialed-in Suspension Tuning Expect the chassis and suspension to be optimized for sharper reflexes and handling. Massive Brakes Giant brake discs and calipers supply fade-free stopping power. High-Performance Rubber Bespoke ultra-high-grip tires connect the prodigious power to the road. Driver-Focused Setup The steering, suspension and brakes aim squarely at an intense, rewarding driving experience. Cruising Comfort A more pliant suspension mode maintains composed comfort when desired. Target Customers and Competitive Set Well-to-do driving fans comprise the target demographic for Fisker's opulent new halo model. Luxury EV GT Segment The Ronin competes among upcoming luxury electric grand touring convertibles. Key Rival Automakers Polestar, Genesis and Tesla all aim for the same affluent consumer base.

Tech-Savvy Early Adopters Wealthy technophiles will be drawn to the carbon-conscious yet extravagant sports car. Brand Cachet Fisker must elevate its brand prestige to match established luxury marques. Expected Pricing and Availability The 2026 Ronin will command a substantial sum consistent with its positioning and exclusivity. Production Timing Manufacturing should start in late 2025 for the 2026 model year. Base MSRP Pricing initiates at $385,000 before options or delivery charges. Reservations Open Now Fisker welcomes $2000 deposits to reserve build slots immediately. Ultra-Limited Numbers Strictly capped annual production will maintain the Ronin's elite status. FAQs What is the Ronin's body style? It's a 2-door coupe with rear-hinged rear doors for easier cabin entry and exit. What range can it drive on one charge? Fisker targets approximately 600 miles between charging stops. How quick is the Ronin? With 1000 horsepower, 0-60 mph happens in around 2 seconds. Top speed exceeds 200 mph. Does the roof retract? Yes, the carbon fiber roof panel folds away to allow open-air driving. When can I purchase the Ronin? Production commences in late 2025, with initial deliveries in 2026. Reservations are already open. #Wiack #Car #CarInsurance #CarRental #CarPrice #AutoLoans

[didanawisgi]

I’ve been doing a lot of research work lately on potential (yet unknown) Phase Transitions (Beyond Liquid, Gas/Vapor and Solid/Ice) of Water and measurement of the respective Dihedral Angles of water molecules through these transition phases and what this might mean for the clustering Geometries.

The Dihedral angle of Snow (which is differentiated from ICE/Solid) is not presently confirmed/known leading to the mystery of why Snow takes the shape of perfect hexagons particularly when none of the various phase Dihedral angles are even remotely close to 120°.

An argument can be made for 108° Dihedral angles enabling hexagonal matrices as 360° / 3 = 120° and 360° / 3.3333… = 108°, where 3.33333 represents an infinitely mirrored fractal of the number 3. This phenomenon is also true for all other numbers like 6: 360° / 6 = 60° (Hexa angle) ; 360° / 6.6666… = 54° (Penta angle (54°*2 = 108°).

The Water Vapor Dihedral = 111.5°; the Water Liquid Dihedral = 104.5°. The Mean Angle = 108°.

One other consideration: as Water represents such a significant aspect of the superstructure of DNA 🧬, does the above inherency of Water toward BOTH the Hexagonal and the Pentagonal geometric associations point to potentially why the nucleotide pairs (Adenine+Thymine; Cytosine+Guanine) of DNA are precisely Hexagonal and Pentagonal geometries?

Further, what other implications might the greater understanding of Water’s various Dihedral Angles portend to understanding the different phases of Water. Moreover, in a broader sense, are the transition phases of molecules (such as Water for example), actually DEFINED (perhaps entirely) by the transitions in their geometric dihedral angles?

If there is indeed a Fourth (or more) Phase of Water as Water Researcher Gerald Pollack posits, are there more (yet unknown) dihedral angles of Water’s subtle transition phases and therefore more to understand regarding both Genotypic and Phenotypic Expression?

“Applied Geometry = Physics. Applied Physics = Chemistry. Applied Chemistry = Biology”

[arcanumblog]

RT @andtartary2: In Wyoming, USA, there is one unusual place known among extreme climbers on the Dihedrals Wall cliffs. On the route there is a megalithic block, machined in the shape of a cube. The cube is not small, the height - 23m, two faces processed at an angle of 90 °, lies at the foot of… https://t.co/b36xWxjMwC https://t.co/1btrq3hc3J

RT @andtartary2: In Wyoming, USA, there is one unusual place known among extreme climbers on the Dihedrals Wall cliffs. On the route there is a megalithic block, machined in the shape of a cube. The cube is not small, the height – 23m, two faces processed at an angle of 90 °, lies at the foot of… https://t.co/b36xWxjMwC https://t.co/1btrq3hc3J — 🅐🅡🅒🅐🅝🅤🅜 (@MenteDesordena1) May 13,…

[picturekites]

Coracias - Construction

Originally I made this kite with a three point bridle, however, it was incredibly difficult to find the perfect symmetry and it would fly to the side. I changed the bridle system to a two-point bridle which instantly improved the kite's performance and reduced the setting up time prior to each flying session.

The kite's sale was originally held together using Venture Tape, however, after its completion I had access to an old (and reliable) sewing machine which I then used to reinforce the sail laps. A zigzag running stitch was used to sew the sail laps. With the sewing machine to hand, I travelled the perimeter of the sail installing a hem as I went. The hem gives the kite a neat look as well as reduces the stretching of the kite sail.

The webbing pocket at the bottom of the spine had been penetrated by the fibreglass spar during one flying session and so it had to be fixed by doubling up the webbing. I believe one layer of polyester webbing would be sufficient, however, the Nylon webbing I have used is thinner and allows greater movement and stretching between the threads.

To maintain the symmetry within this kite I had sewn in some small guidance pockets for the central spine to go through. The guidance pockets restrain the sail from sliding sideways around the spine.

Materials

60gsm Ripstop Polyester

6mm Venture Tape

5mm Fibreglass Tube Spars

5mm End Caps

5mm Nocks

5mm Plastic Dihedral Connectors

25mm Hook and Loop

25mm & 50mm Dacron Tape

25mm Nylon Webbing (Use Polyester Instead)

4mm Eyelets

3mm Bungee Chord

35daN Bridle Line

22daN Flying Line

[adammccrabbe]

These are two technical drawings I have completed, both involving finding and calculating the dihedral angle. They were complex but I enjoyed the challenge, and once I got the swing of things they became easier