Points to note -
(a) there is a bunch of limits (two of which are ASD and TOD) EACH of which is looked at in isolation to determine a maximum takeoff weight. (The skill bit lies in the juggling process to end up with the best limiting weight).
(b) some of these limits are affected by V1 selection and optimising each may well require a range of V1 values
(c) with respect to (b) a range of V1 values is not much use for a given takeoff schedule so the usual operations engineering aim is to find that ONE V1 value which, when plugged into each separate calculation, gives a set of takeoff weights such that the lowest within the set (the "limiting" case, as we are wont to say) is as high as we can achieve.
It follows, for a given RTOW table, that we might well end up varying the V1/Vr ratios across the table. Although this usually becomes overly onerous if the process is being done manually .. with an AFM model on the PC .. no probs ...
One advantage of doing a lot of manual calculations is that one gets a VERY good feel for the underlying ebb and flow of the optimisation process.
(d) keep in mind that, as soon as we introduce clearway, we MUST consider TORA and TORR so that we don't end up with grass, dirt, lights and aerial structure in the tyre treads ...
(e) some folk probably get a tad confused when the AFM charts "appear" to be ignoring or somehow merging different limits. This is just an artefact of the graphical presentation techniques .. at the end of the day, EACH relevant limit is being considered and built into the overall calculation.
Simple questions such as "what does such and such varying do to V1 ?" necessarily can only be answered simply by stating (or inferring) various limitations on other boundary conditions. Generally I find such questions more confusing than illuminating for the educational process unless those other boundary assumptions are clearly stated. As they say, the devil is in the detail and I can present two apparently different stories for many questions if I am selective in the boundary conditions applying.
Having played with a number of aircraft for which clearway becomes very critical in optimising TOW the following may be useful to consider (but keep in mind that I can make a slight change in the assumptions and the story necessarily then may change to a greater or lesser extent)
(a) from whatever starting point where we have a given weight from the sums ..
(b) if the TO is ASD-limited, then there is no option to increase V1 without reducing weight .. which is not the aim of the game. (It is presumed that the TO has been optimised to the extent that the figures are near limiting for the TOD case - if not, why not ?).
However, if we get a bit more TODA by introducing or extending clearway, then we can look at reducing V1 a little which MAY allow us to juggle a resulting small increase in ASD-limited TOW provided that one of TORR and TODR doesn't then immediately become limiting.
(c) if the TO is TOD limiting, then the increase in TOD should give an increase in TOW due to the extra TOD or MAY allow us to increase V1 a little and get a bit more TOW providing that neither of ASD/TOR immediately becomes limiting.
(d) if the TO is TOR limiting, then we can only look at increasing V1 to improve TORR, providing that ASDR doesn't immediately become limiting.
However, one would expect that this option had been exploited fully first time around so, in reality, TOR-limited cases ought not to respond to an increase in clearway.
(e) if nothing were limiting first time around, then we could have increased/decreased V1 as appropriate until one case became limiting in such a way that we ended up with an optimised (ie maximised) TOW. If then we can get some more clearway, we could revert to (b) or (c) and maybe tweak a bit more weight out of the calculations.
For any runway analysis it is very much a case of juggling things a bit this way or that to end up with something becoming limiting but in the way which gives us the maximum RTOW for the chart. Sometimes one can spend quite a lot of time on this iteration process .. hence the reason we all loved the advent of microprocessors to do the slave labour numerically intensive bits of the exercise.
If the above is confusing, either OS or I can run up some pictures to help clarify the words.
How can a take off be accel stop limited in isolation?
Quite easily.
Find a runway with a given set of ASDA/TODA/TORA .. when you do the sums for a given set of ambient conditions, you will find that each results in a particular maximum TOW. Once ALL the various sums have been done, the lowest resulting TOW becomes the limiting TOW for that particular set of ambient conditions.
This set of weights will have a predictable relationship depending on the particular Type and that predictable relationship may well be very different for another Type.
If the ASDR ends up being the limiting factor (ie results in the lowest TOW) then the TO becomes ASD limited.
I can always stop below v1 so by reducing v1 i can declare a higher stop limited weight.
Very true .. but the down side is that the TODR/TORR increases and that might prove to be less than useful.
For the go case as weight increases for a fixed TODA v1min must increase.
True - due to increasing Vs unless I am missing your point ? Alternatively, once TODR (or, if you prefer, in this case, TODA) becomes limiting, we can only increase that limiting weight by increasing V1 with the caveat that ASDR may soon become the limiting problem.
If I plot the go line and the stop line where they cross must be the OEI runway limited weight.
If we are only considering ASD/TOD.
adding clearway moves the go line such that i can have my failure at a lower speed and still go. Now where the go and stop lines cross is at a lower speed (v1) and a higher weight.
However, as soon as you start going down this path we also need to be looking at ASDR, TORR as well as TODR - one will become the limiting case. Much easier to present this discussion with some graphs to illustrate the considerations.
Clearway has no effect on V1 max but will reduce V1 min so long as it isn't limited by something else. (VMCG)
But note that increasing clearway may permit an increasing V1 until either TODR or TORR becomes limiting. It can be rather confusing to folk if we ignore the TOR consideration ..
For a given takeoff weight, any increase in V1 leads to a reduction in both TODN-1 and TORN-1. The reason is that the all engine acceleration phase is longer with a higher V1 speed, and, consequently, in case of an engine failure occurring at VEF, the same V2 speed can be achieved at 35 feet at a shorter distance.
I think I would be emphasising things a little bit differently. Yes, the AEO distances up to the failure point will increase somewhat. However, the main consideration is that the OEI distances between a lower V1 and the nominated Vr will be SIGNIFICANTLY greater than between a higher V1 and the same nominated Vr. (Note, also, that Airbus are including both TOD and TOR in their discussion).
But it's saying the same thing. Increase V1 leads to reduction in TOD n-1 is the same as increase TOD n-1 leads to reduced V1.
.. but not a useful observation when considering what a varying clearway might be doing to the calculations .. except to the extent that the comment has relevance to juggling V1 in the presence of clearway to get a better ASDR/ASDA margin at the same weight. I think that you might be missing the underlying point that the aim is to increase TOW in general.
The driving point in the discussion needs to be that, in the presence of whatever I have in the way of runway etc. lengths, the aim is to juggle V1 to maximise TOW.