Anyone got any suggestion why my estimate of ISS speed was so overstated? Have I missed some obvious assumption, or is it merely because I've assumed it to pass directly over, when it's some 50 degrees south and west of me?
Welcome to ApolloHoax, Apollo 957. I think your reply No. 315 might be way above Neil Baker's ability to comprehend it. In fact I wonder whether he has ever looked up the predictions for visible passes of the ISS for his area and watched it pass over.
I have watched it many times, and often post the details in advance on a New Zealand message board when it makes a good pass for most of the country and there is widespread clear weather. It's always enjoyable to hear people all over New Zealand exclaiming about it, and that the kids waved to the astronauts.
One thing I often try while watching the ISS, is counting off one second and then getting my brain to accept that it travelled over 7 km in that second. Something in my head always says, "Nah! Impossible!" I blame my earth-based existence in an atmosphere for that.
On the night of 29-30 December 2007 I watched the ISS make five consecutive passes, which is apparently a fairly rare sight that few people have seen. Here in New Zealand our air is apparently much clearer than in the northern hemisphere, and I have often seen it with the naked eye when it is 5 or 6 degrees above the horizon.
Back to your question, maths was my worst ever subject at school in the 1950s and 60s, but I think its distance put you wrong. You really need to use a pass that's as close to overhead as possible, 80° elevation or better.
Below are the figures for its closest pass for me on 10 July 2015, when it reached 85° elevation. The sky was light in the northwest, but had it been darker and the ISS visible when at 10° elevation, it would have been visible for about 6 minutes 25 seconds. I'll include my entire post about it. The figures at the bottom are from the Heavens-Above website and modified a little for laypeople, and other details come from the ground track map and an atlas.
http://www.heavens-above.com/International Space Station tonight 10 July 2015
The ISS crosses central New Zealand tonight, northwest to southeast and offshore from Taranaki and Wanganui, then directly above the southern Manawatu and Wairarapa.
Easily visible (if skies are clear) from between lines from Auckland to East Cape and Hokitika to Christchurch, and low in the sky from further away.
The sky might be too light to see the ISS when it's low in the NW, but if so, it should be visible higher up and in darker sky around 5:51:00 to 5:52:30,
5:52:50 pm onward, passes along and above the Taranaki Bight, just offshore from Opunake, Hawera, Patea, Waverly, Wanganui and Ratana.
5:53:14 passes above and between Himatangi and Foxton on the Manawatu coast.
5:53:27 crosses the Wairarapa coast near Castlepoint.
5:56:15 pm – Enters Earth's shadow E of Clutha, SE of the Chatham Islands.
Figures for Manawatu
5:47:52 pm – Rises (not visible yet) – NW – 2,315 km distant
5:49:56 pm – Reaches altitude 10° (becoming visible) – NW – 1,463 km distant
5:53:12 pm – Maximum altitude 85° – SW – 415 km distant
5:56:15 pm – Enters Earth's shadow, altitude 12° – SE – 1,361 km distant