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In my alternate Earth, which follows our timeline almost consistently, I want one of the differences being that the de facto standard for cars is that they have rear steering wheels instead of the front steering wheels we have. With rear steering wheels I mean the two back wheels which give direction to the vehicle.
What single change in the (technology) history would make this happen?
The earliest the change, the better.
Rear-steering wheels are dynamically unstable, that is, when the car is moving forward, any small misalignment of rear wheels position vs fixed front wheel axis will cause a force that would turn them to the side they've got turned. This is an unstable equilibrium and will not last long enough without any control. Yet, should one of those people trying to drive such a car EVER drive backwards, he will discover that the controls are now easier, with the result of front-steered car. Therefore, what you ask for is plain impossible.
As Vesper already pointed out, front-wheel steering is far superior. So if left to develop freely, cars would quickly converge on that. The solution must be in society then, not technology. We already have laws that prevent use of technology by society in general: Patent laws.
In your alternate history "alternate Edison" has successfully lobbied for strong and perpetual patent laws. These give total control to the patent holder. Now, "Lightning" front-steering has been patented by some misanthropic inventor that feels the masses should not be allowed to enjoy his inventions. He only licenses it for the production of supercars etc.
The entire car industry has then banded together to create an international standard based on a rear-steering bar (RSB) that has become the global standard.
The only way to drive a rear steering vehicle without constant high levels of attention and continual steering inputs is if the steering is actively stabilized.
This need not require electronics, as we might tend to think today; a "fifth wheel" under the center of the vehicle can act as a combination of stabilizer and steering controller, giving the stability of well designed front steering and the maneuverability of rear steering. The linkage, being all mechanical, might well date back to the Renaissance (equivalent) or even Classical period, whenever someone was clever enough to invent this.
However, rear steering doesn't fit well with vehicles pulled by animals, so there might also be a case where the inventor had a very skittish cart horse, and invented a way for the horse to push the cart while remaining enclosed in a lightweight "stall". Tiller steering (which evolved into a steering wheel, eventually) allows control of the horse without dealing with long reins and the slack in them.
Yes, the system is complex -- but first is best might well win the day, or the "sheltered horse" carriages might have competed with "horse-tail" types up until someone needed to mount a large, heavy steam boiler where one person could both tend the fire and steer the machine.
Should also note, from comments, that Cugnot's tricycle, the very first steam powered land vehicle (first "automobile") was front drive and front steering -- but if Cugnot's valve gear had been opposite phase, his engine would have rotated the other way and it would have been rear drive and rear steering. I recall another very early steam automobile that was a converted boat, driven by the main wheels but steered with a smaller wheel mounted on the rudder (would have been pretty cranky without a differential, though).
A rear-steering car is an example of an inverted pendulum, which as many have mentioned is inherently unstable and infamously difficult to control. Using this design will make cars more dangerous, will require roadways to be significantly wider, and will limit how quickly your vehicle can turn. If you really want this in your world, though, here's a way you can contrive it into being:
Henry Ford didn't return home when he was 19.
At age 16, Ford left home to work as an apprentice machinist for several companies in Detroit. He returned to the family farm three years later, where he worked for almost 10 years on a farm and a sawmill until he became an engineer for the Edison company. It was here that he developed his quadricycle, the precursor to his automobile.
In your world, Ford never returned home. Instead, he continued to work in Detroit, where his last employer was Dry Dock Engine Works, a manufacturer of engines for boats. Ford stayed here longer in your world, where he advanced to become the chief test pilot and analyst for new engine designs. He spent many, many days piloting small craft around the Detroit River, and he particularly enjoyed the tugboat that they used for testing cargo hauling capability. As a result, his automobile designs did not evolve from the horse-drawn buggy. Instead, he took a wildly-successful tugboat design and modified it to operate on land.
The resulting vehicle would be built in a radically different manner. Your cars would look more like this photo of a tugboat pushing a barge:
The driver would sit in a small cab, most likely alone, with the engine and controls. This cab would link up to a payload of some sort, whether that be a passenger compartment, flatbed for cargo, etc. and would push it along. The payload section's basic frame would be structured somewhat like of a train car: a flat platform with its own fixed wheels, but dependent on external propulsion and steering.
All of the complex, expensive machinery is encapsulated within the cab. Customers could buy a single cab, plus several relatively-inexpensive payload units which would allow them to easily haul cargo, take their family to town, or even do light farm or industrial work without having to buy separate vehicles. A delivery driver could drive a box truck, a liquid tanker, and a refrigerated food van in a single day, all without leaving his cab. Ford was also known for his standardized designs, which allowed customers to upgrade to a newer cab design while still using their existing payload units.
Engineers would undoubtedly notice the inherent stability problems with this arrangement once speeds increased to a certain point. However, Ford's design was ubiquitous and deeply entrenched by that time, and the existing ecosystem of cabs and payload units meant that redesigning the vehicle for higher speeds would require customers to abandon their extensive investments in it. That would make the new designs far too expensive for all but the richest customers, not to mention you'd have to re-train every driver on the road. Drivers were even frightened at the very thought of piloting a vehicle from the front. The payload unit offered good protection in the event of a collision, and moving the cab to the front presented a lot more danger for the driver and for the expensive part of the vehicle. Instead, the existing design stuck, and vehicles in your world have inherent limits to their speed and maneuverability that drivers simply accept as a normal thing.
Early concepts of Greek steam engines are developed and exploited by Rome to build a world-spanning empire. Steam ships and trains come to totally dominate long distance transportation. Wagons and horses are considered backward, quaint, or weapons of war (and thus rebellion). Even wagons come to be run on rails, which are viewed as modern symbols of power and dominance. Open land is used for crops or filled with trees to fuel the hungry appetite for steam power.
So all roads are narrow and twisty, dominated by pedestrians, horses and the smallest and most maneuverable wagons. No one considers roads to be long distance transport, so no one thinks about going fast on them. You want to avoid the many obstacles.
So when cars come to replace wagons and pedestrians, they compete with a massive, standardized global network of trains and rails. Cars put a premium on maneuverability, and speed is not a significant consideration.
The earliest cars had a terrible safety record, but forward-thinking engineers realized that seat belts and rear-facing people prevented deaths. So they decided to make the driver face backwards and drive via a series of mirrors.
The saddle and bridle lobby, eager to quash the horseless carriage, lobbies to make the awkward arrangement mandatory for the dangerous contraptions. This was so successful that governments mandate this seemingly unusual arrangement.
Car engineers add gears in both directions to facilitate driving either way. "reverse" driving is stable at higher speeds, while "forward" driving allows better control and a direct view by the driver at lower speeds.
Mechanical computers in the 1800's lead to an early development of advanced computing power. So by the time cars become popular, they are already self-driving. They start with dynamic control, and rear steering is adopted as the standard.
Your cars arise from shipping design not horse carts. Ships are steered from the rear, so if the first mass produced car was created by maritime enthusiast or in a society with a much stronger maritime tradition, that is what they would make because that is the form of steering most people are familiar with. Keep in mind early automobiles were steered by tillers so its not even that far fetched, the tiller linkage can just as easily go to a back wheel as a front wheel. It does not even require that major of a redesign to just swap the direction of travel so you can use early cars as models.
Keep in mind early cars are slow, so high speed performance issues will not have a chance to have an effect, problems later on will not be able to reverse the design.
It doesn't matter if the design is better or worse it just need to dominate the early market. Once it becomes common cultural inertia sets in and rear steering front end drive cars is what gets made from then on regardless. Because that is what people will know how to drive any attempt to try something different never gets a chance. Its the same reason the Qwerty keyboard is the keyboard we still use and why we use a dangerously narrow railroad gauge. It is how countries lock in electrical plug or which side of the road you drive on. A lot of technology has horrible inefficiencies that are just baggage from early designs and changing them is just too much trouble because it requires retraining the users. One fun side effect is rear steering bicycles would likely also become the standard.
Without changing physics. We change need. Horses never made it out of North America and so went extinct. The carriage was never invented and standard road widths were human push cart widths, not carriage widths. Although other creatures were domesticated none performed as well as horsed would have or adapted to their domesticated role poorly. City's became more compact. When the gas engine came about it needed the maneuverability of the rear wheel steering to navigate the narrow streets built up over centuries. Custom became standard.
where speed became a need in inter urbane/city travel. A method of the driver turning around and driving the car at higher and safer speed was devised.
Naturally the whole design of the car will need to change since the road width limits the cars width to under 5ft wide or less! I would not be surprised if in city driving the driver would sit in the rear behind 2 row seats in front of him and drives from the rear, until he needs intercity speeds where he turns the cockpit around and then is driving from the front. This is all weird and almost Rube Goldbergish, or might not be surprised to see a cat in a hat driving...but it checks the boxes.
As Vesper's answer notes, the laws of physics dictate that front-steering cars will cause a lot fewer accidents, due to stability.
One way to make rear-steering cars safe is to make them trams. This is sort of cheating, because trams are not really cars. But imagine a society where there are tramways on every road: it would be infeasible to have switches at every junction in the track, so the junctions are just open and the tram must be steered onto the branch the driver wants to go down. (There are probably also not as many junctions as a typical road network has.)
In this case the main safety risk is that the front wheels will go down one branch while the back wheels go down another, so it actually makes sense to give more control over the back wheels than the front: that way if the front wheels take the wrong branch by mistake, the driver can more easily apply a force on the back wheels to take that same branch. (Perhaps there is also some mechanical feedback built into the steering system to make this happen automatically.) Taking wrong turns would be more likely, but the front and back wheels going down separate tracks would be much less likely, so it trades inconvenience for safety.
So what single change in history would cause every city to have tram lines on their roads? Perhaps if people had started taking the threats of air pollution and climate change seriously a lot longer ago, society would prefer trams because of their lower emissions. Here's a not-entirely-implausible sequence of events:
This gets you to a modern society where most people drive "cars" that can only follow tramways in the roads, and those cars can have rear steering as standard.
Just to add to assorted comments why rear-wheel steering outside of certain specialized vehicles isn't a thing, here's an example of why: the 1933 Buckminister Fuller designed Dymaxion Car.
Leaving aside the issue of the bad aerodynamics making it dangerous to drive, here's a video of someone driving one. While one of the problems noted would have been dealt with with two rear steering wheels and not the one, the control issue would not have gone away because of the steering. Basically, at over 40 mph the thing is a danger.
https://www.youtube.com/watch?v=N1yxFDvqALI
And here's a useful experiment I saw someone describe to explain the issue with rear-wheel steering: the next time you're at a grocery store or some other place with a shopping cart that has two fixed wheel and two on casters for steering, try pushing it around the store backward for a while and you'll begin to see some of the issues.
Cargo cult
Your civilization didn't invent cars, they learned about them from another advanced civilization that left some car kits on your planet/continent. But the instructions were confusing and written in a language your people don't speak, so they did the best they could. Maybe it didn't come out looking like the diagram, and there were some extra screws, and steering is kind of a pain, but it was better than riding donkeys. Eventually people figured out that front steering works better, but by that point cultural inertia, blah blah...
Religion
The society is extremely religious and there is sacred symbolic importance to the steering orientation, that is more important than safety/convenience/money. Perhaps this would evolve from a naval culture where helmsmen were toward the back of the ship, or a military where generals were in the rear. The Christian Church once condemned left-handedness, perhaps this culture would equally condemn front-wheel drive or front-wheel steering.
Digitigrade legs
Okay, this is a big change, but...
In terrestrial vertebrates, digitigrade locomotion is walking or running on the toes (from the Latin digitus, 'finger', and gradior, 'walk'). A digitigrade animal is one that stands or walks with its toes (metatarsals) touching the ground, and the rest of its foot lifted. Digitigrades include walking birds (what many assume to be bird knees are actually ankles), cats, dogs, and many other mammals, but not plantigrades or unguligrades. Digitigrades generally move more quickly and quietly than other animals.
Digitigrade legs (as found in birds, dogs, and many others) are much more nimble, usually resulting in faster and quieter animals than platigrades like us. Perhaps to a digitigrade hominid, super-sensitive rear-wheel steering would feel natural.
A rear-steering car IS NOT an inverted pendulum.
The only thing that affects stability of steering wheel position is inclination of steering axle.
A wheel with perfectly vertical steering axle is in neutral equilibrium - there is no force that opposes / promotes turning.
In practice king pin inclination is used to stabilize wheels in one or both of the following ways:
axle is turned inside/outside, so when wheels are straight the car is at the lowest position, so you need to use a little force to turn a wheel to side and there is small force that returns it to neutral position without use of any springs.
and/or axle is turned backwards a little, so centrifugal force during turn straightens the wheel.
If second way is used then steering of normal car may feel unstable during fast reverse driving, since in this case centrifugal force would destabilize the wheel, but that has nothing to do with "inverted pendulum" and easily fixed for rear steering wheels design.
The real problem is that when normal car turns then it's front begins the turn immediately.
It is bad for parking in small place - that's why we use reverse parking for that (and your rear steered car would be easy to park for novice driver).
BUT it is good when you want to avoid obstacle / pedestrian while driving fast - rear-steered car will need higher lateral acceleration.
In frontal steered car frontal part is accelerated first during turn - the one that avoids obstacle. In rear steered car - back part is accelerated first and to the wrong side. So it needs more acceleration to avoid obstacle and skid is more probable. Rear-steered car can make sharper turns but at high speed maneuverability is restricted by skid.
Also you need to put driver at the back - that would make a little harder for him to notice obstacles, or add long (and costly) axle to turn rear wheels from front.
That would make rear-steered car more dangerous and no "actively stabilized steering" would be able to help with that.
So you need to find a way to make good maneuverability of rear-steered cars at slow speeds much more important than their bad maneuverability at fast speeds.
Two things together:
In other words, no rear-wheel drive cars with front engines or front-wheel drive cars with rear engines + cars mandated to have rear engines for safety + steering on drive wheels = rear steering.
No Power on the Wheels
Your Society didn't figure out how to get Power to the Wheels. Instead they use Rocket Boosters to accelerate and for the first fifty years the rocket cars were only used on straight ways so there were no big deal to steer with the tires.
During the invention time the world wasn't that populated and the major cities are fare away from another. So the rocket-cars started as public transportation like trains in our world, but faster and without rails. When the surface of your planet got more populated the cars needed a possibility to steer around some objects. Steering was made by pushing a break into the ground; and that's easier to control if you break in your rear part.
When they had to make slower vehicles to support more nearby cities, they stayed with sliding and rear steering as long as they could. That's where technology is today.
The main technology comes from an very icy region (like Antarctica) where they don't need wheels. So the whole invention took another way.
I guess in future they will discover things like front steering.
Glass was never invented, thus no windscreens are available.
To avoid bugs in the face, passengers sit facing backwards, like a rowboat.
Depending on technology level, bumpers, mirrors or electronics deal with collision avoidance.
Weak (or governed because of emissions concerns or safety rules) coupled with something like narrow 90 deg car parks (perhaps due to car population explosion meant driving forwards with visibility and rear steering useful, but no reason to change to front.
As others pointed out cars with the steering wheels on the rear are unstable, but that could be part of the fun. In the Stout Scarab the suspension were attached to the car body above the centre of mass and this gave the car an unusual behaviour, in the turns it leaned towards the inner side of the curve like motorcyclists do. With some extra struts and reactive joints the wheels might, also, lean a little bit. That would make a car a little bit more stable, but still prone to skidding. After all when you have the steering wheels on the rear it turns like a boat and getting the momentum for a skid is easy.
Such a car would be fun to drive, but it would not be for everyone, so you can imagine a world where most of the people use public transport, only few expert drivers use the private car.
How did we get there? A period of freak weather left the roads muddy or icy, but always slippery. Trams and train became so successful that they took over the bulk of the transport system. The roads were left to few drivers that took the habit of skidding at every turn like in a speedway race. When the weather stabilised the habit remained and drivers wanted cars prone to skidding.
The alternative story
I also thought about a world with small and crammed roads. All turns must be done in narrow spaces with little visibility, but in such context probably 4 steering wheels would be the best solution.
Unless most of the cars are cheap pick up trucks with the cargo on the front because thefts are frequent and the driver must keep a constant watch on it. With little visibility to make tight turns and the rear wheels closer to the driver position, the rear steering wheels became the easiest and cheapest solution.
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